Hello, everyone. So, we have now entered in this coordinate geometry section. Basically, you can say. So, in last class, we discussed about circles, some basic questions of exercise one. So, today we will move forward to the next exercise exercise two of the circles. So, let's start. So, this is our first question. It is saying if the line x plus two lambda y plus seven equal to zero is a diameter of the circle, x square plus y square minus six x plus two y equal to zero, then the value of lambda is. So, one circle is given, and it's diameter is also given the equation of the diameter basically. So, we have to find this value of lambda. Okay. So, let me write the equation of a circle. It is x square plus y square minus six x plus two y equal to zero, right? So, we can identify the center of the circle, right? Center will be minus g comma minus f. So, we can say three comma minus one, right? Three comma minus one because two g is minus six here. So, g becomes minus three and two f is two here. So, f becomes one. So, our center is minus g means minus of three is three and minus of f means minus one. Now, this is the center of the circle, right? Now, it must lie on the diameter and we know the equation of diameter. Diameter is given as x plus x plus two lambda y plus seven equals to zero. Now, this point must satisfy this. So, put the value of x and y here. So, three plus two lambda, what is y minus one plus seven is equal to zero. So, this will become ten minus two lambda is equal to zero. From here, we get lambda is equal to five. Okay. So, this is our answer. Lambda equal to five. So, option C is correct. Let's see the next question, question number two. If one end of diameter of the circle, this is minus one comma two, then the other end of the diameter is. Okay. So, equation of circle is given. It's one end of diameter is given and we are asked to find its, find the other end of the diameter. We have to find the coordinates of other end of diameter. Okay. So, let me write first the equation of circle. It is saying two x square plus two y square minus four x minus eight y plus two is equals to zero. So, okay, let me first make the coefficient of x square and y square as one. I have to divide by two. So, it will be x square plus y square minus two x minus four y plus one is equals to zero. Okay. Now, we can say the center of this circle. What will be the center? That will be one comma two. Right. One comma two will be the center of this circle. Now, let me draw the circle itself. Let me draw its diameter also. Now, one end, let this AB be the diameter. Let this AB be the diameter. We know the one end of diameter that is minus one comma two. Okay. And we have to find the other, the coordinates of this B. So, let me assume it as A comma B. And we know the center of this circle. What is that? One comma two. The center of this circle is one comma two. So, if AB is the diameter and this is center C. So, this AC will be equal to BC. Right. So, C will be the midpoint of A and B. So, we can say this AC must be equal to BC. Okay. Both are radius only. So, AC equal to BC. Now, I will, how can I find the midpoint of this AB? This will be minus one plus A upon two. And that is nothing but that is equal to one. Okay. And this two plus B upon two is equal to two. Right. The coordinates of this C. So, from here I get minus A plus one is equals to two. Or we can say A is equal to three. And what will be B from here? Two plus B is equals to four. So, B will be equal to plus four minus two, that will be two. So, three comma two. Three comma two will be the coordinates of B. So, this will be our correct answer. Option number B. Right. So, moving ahead, let's see question number three. It is saying if a circle passes through the points, zero comma zero, A comma zero and zero comma B, then the centers, then the center of the circle is. Okay. Means the circle is passing through origin basically. So, let me draw this sketch, what is given in the question. This is our circle. And let me consider this as coordinate axis. Okay. So, this will be the zero comma zero point. Sorry. This will be zero comma zero point. This point will be A comma zero. And this point will be zero comma B. Right. And what it is saying, we have to find the center of the circle. Okay. We have to find the center of the circle. So, center of the circle will be basically, if you say this will be our diameter. Sorry. So, this point, this, suppose I am taking it as B and this is as A. So, AB will be our diameter. Right. And what will be the midpoint of this? The midpoint of AB will be the center of the circle. So, we can easily find the coordinates of this C. C will be nothing but A plus zero by two. And the coordinates, the X axis, sorry, X coordinate of C will be A plus zero upon two. And Y coordinate will be zero plus B upon two. So, X, we can give the coordinates of C as A upon two comma B upon two. Okay. Why this is, why this AB will be diameter because it is making this AB is sustaining the 90 degree at the circumference. Right. Why 90 degree? Because both these are, what you said, both this, this is Y axis, our Y axis, we can consider this as Y axis and this as X axis. Hence, this AB will be the diameter and C will be the midpoint of this AB. And by this, we find the coordinates of C as A by two comma B by two. Okay. So, let's take the next question, question number four. A circle passes through the points minus one comma three and five comma eleven and its radius is five. Then its center is. Okay. So, it is saying the question has provided two points from which the circle is passing and we also know the radius of that circle. Okay. So, suppose this is our point A whose coordinates are minus one comma three and one more point is given as B whose coordinates are given as five comma eleven. Okay. Circle is passing through these two points and we also know the radius of that circle is as five. These three things are given in the question and now we have to find the center. Okay. One, like the radius is known to us, radius is given as five. So, let me check the distance of AB, like what is the length of AB? Okay. Like one intuition is coming in my mind like it may come as 10. Why? It may, and if it comes as 10, then this AB will be the diameter. Right. So, once we can arrive at that thing, then we can say the midpoint of this AB will be the center of this circle. So, let me first find the distance, this length of AB. The length of AB will be under root five minus minus one pole squared plus eleven minus three pole squared. That is six squared thirty six plus eight squared sixty four under root. So, yeah, it's true. The AB is coming out to be ten unit. AB is ten unit. It means AB is the diameter. Right. AB is the diameter and if AB is the diameter, AB is the diameter of the circle. AB is the diameter. So, center will be midpoint. What will be the center midpoint of this AB? That means minus one plus five upon two comma three plus eleven upon two. This will be the coordinates of the center. That will be five minus one four by two. That will be two comma seven. Eleven plus three, fourteen by two, center. So, this will be the coordinates of the center. Two comma seven. So, option C is correct. So, we are done with this question. Question number four is done. Now, let's move to question number five. Now, it is saying the radius of the circle having center at two comma one, whose one of the chord is a diameter of the circle, this. Okay. So, let me draw a sketch for this question. It's saying one circle is there. So, this is our circle. The radius of the circle having center at two comma one. Okay. We will draw it for the, whose one of the chord is the diameter of the circle. Okay. So, I'm drawing, going to draw one more, one more circle here. This is the chord of the bigger circle, right? And I think this much sketch is sufficient. We can move with our question now. So, it is saying the radius of the circle having center at two comma one. So, I'm taking this center as O suppose and this coordinates of this O is two comma one, whose one of the chord, like this AB is the chord of the, this circle. So, this AB is now behaving as the diameter of the circle. Means, it is diameter, this AB is the diameter of this circle. The smaller circle and its equation is given by X square plus Y square minus two X minus six Y plus six equals to zero. Okay. So, what we have to find? We have to find the radius of this bigger circle. We have to find the radius of the circle whose center is two comma one, whose one chord is the diameter of the circle. This. Okay. So, this AB is diameter of this bigger, what you said, this given circle's equation means a smaller circle. So, what is the center of this? What is the center of this circle? The center of this circle will be one comma three. Center of this circle will be one comma three and it will lie on AB itself. Okay. Suppose I'm taking this as point as M. So, the coordinates of this will be one comma three and what is the radius for this circle? Radius for this circle will be one is squared plus three is where minus C minus C is minus six. So, one plus nine ten minus six equal to root four. So, radius of this is two. So, this MB we can say, this MB or what you say, AM is equals to two. Okay. So, this unit we came to know at two. And what we need to find? We need to find the radius. Okay. So, let me draw that also. This we need to find it. We need to find this OB. This OB will be the radius of the bigger circle. So, we need to find OB and we know this distance as MB is two. So, we can apply Pythagorean theorem here and we also can calculate this distance of OM. So, what will be OM basically? What will be the length of OM? It will be two minus one is square because we know the coordinates of O and M both. So, two minus one whole square plus one minus three whole square under root. So, this will be one square, one plus minus two square that will be four. So, this will be under root five. Under root five. So, we know OM and we know MB. So, we can entriangle OMR, entriangle sorry, entriangle OMB. We can apply Pythagorean theorem. So, this will be OM square plus MB square is equal to OB squared. And this OB is what we need actually. So, OM is OM squared is five plus MB squared. What is MB squared? MB squared is four that will be equal to OB squared. So, nine is equal to OB squared or we can say OB is equal to three. So, OB is nothing but the radius of the bigger circle that will be three. Three unit, right? So, our answer is option A, three unit. So, let's see the next question. The center of the circle inscribed in the square on y the lines, x is square minus 8x plus 12 equal to zero and y is square minus 14y plus 45 equal to zero. Okay. So, we will draw the sketch for this. Later, this will be circle and this be our circle. The circle is inscribed. So, it will be live within the square. This will be basically our figure. The center of the circle inscribed in a square formed by lines. We have to find the center of the circle. Now, these squares are formed by the line x square minus 8x, x square minus 8x plus 12 is equals to zero. And y square minus 14y plus 45 is equals to zero. This consists of two lines basically. So, x square, we can factorize it as x square minus 6x minus 2x plus 12 is equal to zero. From here, we get x, x minus 6 minus 2, x minus 6 is equals to zero. So, x is equal to 2 and x is equal to 6. These two solutions we are getting from here. And from here, we will get y square minus 5, 9s are 45. So, 9y minus 5y plus 45 is equals to zero.  From here, we get y equal to 5 and 9. So, basically, if you see what, let me name this square as a, b, c and d. So, this a, d line will be basically x equal to 2, right? And this c, d line will be, this c, d line will be actually what you say, x is equal to 6. Okay, this x equal to 2 and this is x equal to 6. And what will be this a, b line? This a, b line will be basically y equal to 5 and this dc line will be y equal to 9. So, our, what will be the length of the sides of the square? It will be 4. This will also 4. This will be also 4. And this will also be 4. Okay. So, now we have to find the center of the circle. So, if I tell what will be the coordinates of a, b, c, d. So, we can say this will be 2, 5. The b coordinates of b will be 6, 5. Coordinates of c will be 6, 9. And coordinates of d will be 2, 9. Okay. And now we have to find the center of the circle. So, it will be nothing but it will be half of this. Means x will be 2 plus 6 upon 2, like if we say c center. So, center will be this 2 plus 6 upon 2 and this 5 plus 9 upon 2. 5 plus 9 upon 2. That will be 4 comma 8 by 2, 4 comma 7. 9, 5, 14 by 2. So, 4 by 7 will be ours. So, coordinates of 4 will be, sorry, coordinates of center will be 4 comma 7. So, option a is correct. Now, coming to the next question, a, b, c, d, a square plus side is a. The equation of circle, circumscribing the square, taking a, b and a, d as the excess of reference. Okay. In last question, the circle was inscribed. Now, in this question, it is saying that the circle is circumscribing the square. So, let me draw a sketch here also. So, this is our square and let me draw a circle, which is circumscribing this. Let me draw it separately. First, I am drawing this circle and I will draw a square inside it. Right? So, what is given in the question? This a, b, c, d, j, a, b, c, d is a square. a, b, c, d is a square whose side is a. Okay. The equation of circle, we have to find the equation of the circle, which is circumscribing the square and taking a, b and a, d as the excess of reference. Okay. So, we have taken a, b and a, d as the excess of reference. So, suppose I am taking the coordinates, taking the a as origin. So, the coordinates of a will be 0, 0. And what will be the coordinates of b? Coordinates of b will be a, 0. Why? Because the sides of the square is of length a. And what will be the coordinates of this d? Coordinates of d will be 0, a. And the coordinates of c will be a, a. So, now we have to find the equation of the circle. So, how can we find? How can we find? Let me join this line segment bd. Let me join this line segment bd. So, what will be the bd? Bd will be the diameter. Bd will be diameter of this circle. Bd will be diameter of this circle. And we know the coordinates of b and d. So, we can write the equation of circles in a diametric form as x minus x1, x minus x2, plus y minus y1, y minus y2 is equal to 0. Okay? If we know the coordinates of the ends of diameter, we can write the equation of circle in this form. So, this is called diametric form. We can say it as diametric form, diametric form of circle. So, equation of circle is written in this way if we know the ends of the diameter. So, what is x1 and x2? So, let me tell this b as x1 and y1. And let me tell this b as x2 comma y2. Okay? So, our equation will become x minus a and x minus x2. What is x2? x2 is 0. So, it will be x only. Then y and minus y1, y1 is 0 here. So, it will be y into y minus a equal to 0. This will be the equation of circles. So, it will become x square minus ax plus y square minus ay is equals to 0. So, this is our required equation of circle. x square plus y square minus ax minus ax minus ay equal to 0. So, option c is correct. Option c is correct answer about this. Let us take the next question, question number 8. It is saying the locus of the center of the circle for which one end of diameter is 3 comma 3 while the other end lies on the line x plus y equal to 4. While the other end lies on the x plus y equal to 4. Okay? And we have to find the locus of the center of the circle. So, we are given with one circle. We are given with one circle. This is our circle. And one end of diameter is also given. So, let me draw diameter of this. So, suppose this is our diameter of this circle. And the one end is one end of diameter is known to us 3 comma 3 and the other end lies on the line. Okay? So, let me draw one straight line here. Yeah, I think sketch is done. We can now this AB, let me assume this as AB. This AB is the diameter. This will be the center. The coordinates of A is given as 3 comma 3. And this B, the other end of diameter lies on the line. The equation of line is given as x plus y equal to 4. Okay? So, B lies on this line. So, what can I take the coordinates of B? Suppose I am taking coordinates of B as A, the x coordinate as A. Then what will be the y coordinate? Y coordinate will be 4 minus A, right? 4 minus A. Since it lies on the line, x plus y equal to 4. Now, what we need to know? We need to find the locus of the center of the circle. So, let me assume this center as C. And let me consider its coordinates as h comma k. Okay? So, A coordinates of A is known to us. Coordinates of B is known to us. Means, it is in terms of A, but it is known. So, we can say, find the coordinates of h, means coordinates of C. So, what will be the coordinates of C, basically? Coordinates of C is h comma k we have considered. So, h will be actually 3 plus, it will be a midpoint of A and B. So, this will be 3 plus A upon 2, right? And what will be our k? K will be actually midpoint of, sorry, 3 plus 4 minus A. 3 plus 4 minus A. Sum of both the coordinates divided by 2. So, 3 plus 4 minus A upon 2. That is equal to 7 minus A upon 2. That comes out to be the value of k. So, what we will do now? We will write A in terms of h and k. And we will then equate what we got, the value of A. So that, and finally we will replace the h and k by x and y. So, from here we get 2h minus 3 is equals to A. 2h minus 3 is equals to A, right? And from here we get 2k, 2k minus 7 is equals to minus A. Or we can say A is equals to 7 minus 2k. Okay. So, from here we can say 2h minus 3 is equals to 7 minus 2k. Why? Because 2h minus 3 is also equals to A. And 7 minus 2k is also equals to A. So, from here we get 2h, 2h plus 2k is equals to 10. Okay. 2h plus 2k, 7 plus 3, 10. From here we get h plus k is equals to 10. Now replace h and k by x and y. So, x plus y is equals to, oh, this will be 10 upon 2. So, 5. So, now replace h and k by x and y. So, we will get x plus y equals to 5. So, the locus of the center of the circle will be a straight line basically. x plus y equals to 5. So, our answer will be option B. Now, let's see the next question. Question number 9. The equation of the circle which passes through 1 comma 0 and 0 comma 1 and has its radius as small as possible. So, two points are given from where the circle is passing and we have to say its radius as small as possible. So, we have to draw one circle. Let us understand this by, let me draw it first. Let me mark it then I will explain. Let me mark this as A, this as B and this coordinates of this as 1 comma 0 and coordinates of B as 0 comma 1. Right. So, this coordinates of A and B are given means of any two points is given. And the question is saying that they find the equation of the circle having its radius as small as possible. So, this yellow colored circle is the smallest circle passing through A and B having A, B as the diameter. Means what I am saying, if two points are given and we have to find the least radius circle, radius of least, sorry, circle of least radius, then A, B that those two points must be the diameter of that circle. Why? Because now let's see this white circle what I have drawn here. Let's see this white colored circle. So, for this is white colored circle is also passing through A and B. Okay, no, but it is not the smallest circle passing through A and B. There will be actually infinite number of circles, circles passing through A and B, but the smallest circle will be that which will be having A, B as the diameter. So, this is the thing in this question. This is what you have to understand. So, I have to write the equation of this circle basically. And we know the diametric ends of this circle. So, we can write this as x minus x1 into x minus x2 plus y minus y1 into y minus y2 is equals to 0, where x1, y1 and x2, y2 are the diametric ends. So, let me write it as x minus 1 into x plus y into y minus 1 is equals to 0. So, this will be x square, x square minus x plus y square minus y is equals to 0, or we can rewrite it as x square plus y square minus x minus y equals to 0. So, this is our equation of the circles. x square plus y square minus x minus y equals to 0. So, option B is correct. So, we are done with this question number 9. Let me take question number 10.  If the points 1, 2, 3, 4, like 4 points are given with their coordinates and it is saying that the 4 points are consyclic, then the value of c. Consyclic means all these 4 points lie on a circle. All these 4 points lie on a circle. So, let me draw and this point, we consider it as A, B, C and D. So, what are these points? 2 comma 0, 2 comma 0. This will, this is 0 comma 1. This is 4 comma 5, 4 comma 5. And this is 0 comma c. This is 0 comma c. So, let me assume this as a center O. So, if you see the distance of all these points from this center will be equal basically and all these will be equal to R. So, all these distances will be equal. That is OA is equals to OB is equal to OC is equals to OD and that will be equal to radius, equal to the radius of the circle. Now, let me find this OA first. So, what will be OA? Or we can say square it. So, OA square is equal to OB square is equal to OC square is equal to OD square. We can say this also. So, we will get rid of this under root thing. So, what will be OA squared? OA squared will be OA squared. Okay. Then in that case, I have to take the, take this as, I have to assume some coordinates of O, no. So, let me take it as a comma B. We can do no. Yeah, we can do because C is here. So, we can take it as a comma in alternate issue. So, OA squared will be A minus 2 square plus B squared. Right? And that will be equal to OB squared. What will be OB squared? That will be A squared plus B minus 1 square. Right?  So, A squared B squared will be cancelled out. A squared B squared will be cancelled out. This will be 4 minus 4A minus 1 plus 2B equal to 0. Or we can say 2B minus 4A 2B minus 4A plus 3 equals to 0. So, this is our first vacation. Let's consider it as first equation. Now similarly, we can say this OB squared is equal to OC squared or OA squared is equal to, OA squared is equal to OC squared. So, what is OA squared? OA squared is A minus 2A squared plus B squared is equal to OC squared. And what will be OC squared? A minus 4 squared plus B minus 5 whole square.  So, A squared B squared is called cancelled. Here we are left with 4 minus 4A and plus 8A plus 10B and plus 16 and plus 25, 35, 41, minus 41 is equal to 0. So, further on further simplification, it becomes 8A minus 4A means 4A plus 10B, 4A plus 10B minus 41 plus 4, minus 41 plus 4 becomes minus 37, right? A is equals to 0. So, this is our equation number 2. From here, we can find the value of A and B, okay? And after finding the value of A and B, what we will do? We will again equate this OD equal to OA or OD equal to OB in A and we will find the equation in C. From there, we can find the value of C. So, this is the motive behind doing all these exercises. So, let me solve it. So, if I add both these equations, this 4A term will be cancelled. So, it will be 2B plus 10B. That will be 12B, right? 12B minus 34 is equals to 0. So, B will be 34 by 12. So, that will be 17 by 6, right? B will be equal to 17 by 6. So, what will be our 4B? 4B will be 2 into 17 by 6 plus 3 is equals to 4A, right? So, this will be 17 by 3 plus 3 is equals to 4A. So, 4A will be equal to 317 plus 320. These three 3s are 9s. Means 17 plus 9 will be 26, right? So, 17 plus 9. 4A will be 317 plus 9, 26, 26 by 3, 26 by 3 or we will get A as 26 upon 12 or 13 upon 6. So, A comes out as 13 upon 6. So, this will be the coordinates of the center of the circle. This O comes out to be 13 upon 6 and 17 upon 6. Now, again equating this value, this OA is equals to OD. We can find the value of C. We can find the value of C from here, okay? You can also equate this OB is equals to OD not an issue. Then also you can find the value of C. So, I think it is clear. I am not taking this forward. So, I am moving to the next question now. So, that will be equal to question 11, okay? So, it is saying the point on a circle nearest to the point 2 comma 1, okay? One point is given. And it is saying the point on the circle nearest to that point is at distance 4 unit. And farthest point is 6 comma 5. Then the center of the circle is, okay? So, if you see, now it is saying this is, suppose this is the point P. This is the point P 2 comma 1, okay? So, let me consider this as point A. Means on extending this line, it meets the circle at A and B. And A is the nearest point. It is at distance 4 units from here. It is at distance 4 units from here. And the farthest point is 6 comma 5, okay? And here one concept is there, like the farthest distance from P will be along the diameter, actually. If PA is the sort, if PA is 4 unit, okay? And A is the point nearest to the P. So, the farthest point will be along the diameter itself. What does it mean? It means that AB must be the diameter. Anyway, we can say the P point will be farthest from P, right? So, PA is given out to be 4. This PA is given out to be 4. And the coordinates of point B is given as 6 comma 5, okay? Then the center of the circle, we need to find the center of the circle, okay? So, this distance is given as 4. So, PA is given as 4. And farthest distance is 6 comma 5. We can find the distance, this PB. We can find this distance PB. What will be PB basically? PB will be 4 square, 6 minus 2 square plus 5 minus 1 square, 4 square under it. So, 16 plus 16, that will be 4 root 2. This PB will be 4 root 2. This PB will be 4 root 2. So, we can say AB will be 4 root 2 minus 4, right? That is nothing but taking 4 comma root 2 minus 1 is AB. That is the length of AB will be 4 into root 2 minus 1, okay? Now, if you see this total distance, this total length PB, right? And A point, if you see, we can say this A point is dividing the line segment PB in the ratio of, from here you see one thing. PA is 4, no? This PA is 4. This AB is, let's understand in this way. This PA is 4. And this, what do you say? AB is 4 into root 2 minus 1, right? So, this PA upon AB. How much it will be? What is PA? PA will be length of PA will be 4. Length of AB will be 4 into root 2 minus 1. So, it will be 1 upon root 2 minus 1. This 4 and 4 will be cancelled out. So, actually this point A is dividing this line segment PB in the ratio of this 1 is to, 1 is to root 2 minus 1. Is it clear? This point A is dividing this line segment PB in the ratio of 1 is to root 2 minus 1. So, we can find the coordinates of A. What will be the coordinates of A basically? This 1 into 6, right?  And what will be the y coordinate of A? It will be 1 into 5, which we can write 5 plus root 2 minus 1 into this thing 1 upon 1 plus root 2 minus 1. This will be the coordinates of A.  So, finally we can write the coordinates of A as 4 plus 2 root 2 upon root 2 and 4 plus root 2 upon root 2. Now, we know the coordinates of A. We know the coordinates of B. Then what will be the coordinate of C? It will be the midpoint, right? It will be the midpoint of this. So, if we say C is the midpoint, C is the midpoint of AB. If C is the midpoint of AB, so it must be equal to the coordinates of C must be. So, let me write it as coordinates of C as A comma B. So, A will be equals to x coordinate of this 4 plus 2 root 2 upon root 2 plus x coordinate of B that is 6 whole divided by 2, right? This will be A. And what will be B? B will be y coordinate of this A.  Our point B, what was that? It's 5, right? So, that will be plus 5 upon. So, this will be our coordinates of the center of the circle, okay? So, on simplification, I guess we get this option as C, 4 plus root 2 comma 3 plus root 2. So, this is our option C. The answer to this question is C, I think. Take the next question, question number 12. The intercepts on the line y equal to x by the circle, x square plus y square minus 2x equal to 0 is AB. Equation of the circle on AB as a diameter is, okay? Let me first draw this sketch. It will be more convenient. Line what it is saying, line y equal to x, no? Suppose we are taking this line y equal to x, okay? This line is y equal to x and this is the circle. So, the intercept on the line y equal to x by the circle. This x square plus y square minus 2x. The equation of this circle is x square plus y square minus 2x equals to 0 is AB, right? This is AB actually, okay? And the equation of circle is given as x square plus y square minus 2x equal to 0. Now, we have to draw one circle, equation of circle on AB as the diameter. So, we have to find the equation of that circle whose diameter is AB. Basically, this thing, this is what is asked in that question. Now, taking AB as diameter, let me draw one circle. Yeah. So, we have to find the equation of this circle, basically. We need to find the equation of this circle. Whose AB is the diameter? AB is the diameter. AB is the diameter for this circle. Okay. So, in the equation of this, let me put y equal to x because y equal to x also lies on the circle. So, if you put y equal to x, we will get x square plus x square minus 2x is equals to 0 or 2x square minus 2x is equals to 0. And again, putting x equal to y, again, here in this equation, we get y square plus y square minus 2y is equals to 0. Actually, what I am trying to do, I am trying to identify the coordinates of A and B. Like, I am solving these two equations now. So, we will get the point of intersection. So, this is what? This 2y square minus 2y is equals to 0. So, solving this quadratic in x, 2x square minus 2x equal to 0 will give me the x coordinate of A and B. From here, we get x1 and x2. That will be the x coordinate of A and B. And from here, we will get y1 and y2, which will be the y coordinate of A and B. Okay. Then, after getting that x1, x2 and y1, y2, we used to write it in form as x minus x1 into x minus x2 plus y minus y1 into y minus y2. So, instead of doing all these things, if we add these two quadratic now, this 2x square minus 2x plus 2y square minus 2y is equals to 0. This will be the required equation of the circle. This will be the required equation of the circle. Why? I am directly adding it. I am directly adding it. Why? From these two equations, we get two values of x. Okay. And that two values will be the x coordinate of A and B. And from here, we get two values of y, y1 and y2. That will be the y coordinate of A and B. Okay. Then, after finding this x1 and x2, I will again make a quadratic by putting x minus x1 into x minus x2 plus y minus y1 into y minus y2. So, instead of doing all these things, I am just adding these two quadratic. Adding these two quadratic, we get the required equation of the circle. So, you can take two common from here. So, x square plus y square minus x minus y equal to 0. This will be our answer. x square plus y square minus x minus y equal to 0. So, this question number 12 is this option A is correct for. Question number 12. So, what is given? Question number 13 is saying, find the equation of circle. The int points of whose diameter are 2 comma minus 3 and minus 2 comma 4. So, it's easy. We have done similar type of questions earlier also. So, 2 comma minus 3 and B minus 2 comma 4. These are the diametric ends. Find the equation of circle. The ints of whose diameter means these are the diametric ints of circle. So, find the center and radius. So, simply we can write it as x minus 2 into x plus 2 plus y plus 3 means y minus y1, y minus y2 is equals to 0. This will be the required equation of circle. So, let's simplify it. It will be x square minus 4 plus y square minus 4 y plus 3 y that will be minus y minus 12 is equals to 0. Okay. So, finally, it becomes x square plus y square minus y minus 16 is equals to 0. Now, what is the center for this circle? Center will be no x term. So, center will be 0 comma 1 by 2, right? 0 comma 1 by 2 will be the center for this circle and what will be radius? Radius will be under root g square plus f square minus c. So, g square is 0. f square is 1 by 4 and minus c. Minus c means minus of minus 16 that will be 16. So, this will be 4 1 plus 64 under root that will be root of 65 by 2. Okay. So, this will be our answer. The center will be this and the radius will be root 65 by 2. So, 13th. Now, let's see question number 14. If 4 comma 1 be an extremity of a diameter of circle, find the coordinates of extremity of the other extremity of the diameter. Okay. So, it's saying let me consider it as a b, a b is the diameter of the circle. So, the points, coordinates of a is given as 4 comma 1. Okay. And we have to find the coordinates of b. Find the coordinates of the other extremity of the diameter. Okay. So, let me consider it as a comma b, but we know the equation of this circle. The equation of this circle is x square plus y square minus 2x plus 6y minus 15 is equals to 0. So, if equation of circle is known means, it means we know the center also. What will be the center? The center for this circle will be 1 comma minus 3. 1 comma minus 3, right? So, this 1 will be the coordinates of c will be 1 comma minus 3. Now, c will be the midpoint of a b, right?   So, a is equals to 2 minus 4 means minus 2. And what will be b? b will be b plus 1 is equals to minus 6. So, b will be minus 7. So, this will be the coordinates of center, sorry, the other coordinates of b means coordinates of other extremity of diameter. Okay. Hope this is clear. So, let's move to the next question, question number 15. It is saying find the equation of circle drawn on the diagonal of the rectangle as its diameter whose sites are x equal to 4, x equal to minus 2, y equal to 5 and y equal to minus 2. Okay. Similar type of question we have done in this exercise only. I think in MCQ, but anyhow here we are not having options. We will do it once again, not an issue. So, this is what given find the equation of circle drawn on the diagonal. Okay diagonal. First, let me write it as x equal to minus 2. I am writing the equation of these lines x equal to minus 2 then x is equal to 4 and this line is y equal to minus 2 y equal to minus 2 and this is y equal to 5. Right. So, let me name it as A, B, C and D. So, coordinates of A will be, coordinates of A will be minus 2, x coordinate and y coordinate minus 2. What will be the coordinate of B? It will be 4 comma minus 2, coordinate of C will be 4 comma 5 and coordinate of D will be minus 2 comma 5. So, this will be the coordinate of D. Now, we have to draw one circle taking diagonal as the diameter, right? Find the equation of circle drawn on the diagonal of rectangle as its diameter. Yeah. So, it is saying that this is, this will be the diagonal of rectangle, right? So, considering this AC as diameter, considering this AC as diameter we have to draw one circle. Okay. So, this equation of this circle we have to find out, equation of this circle we need. So, we know the diametric and this AC will be nothing but diameter, no? This is the diameter of the circle and we know the coordinates of A and C. So, we can write it as x minus x1 means minus 2. That will become x plus 2, x minus x1, x minus x2 plus y minus y1. That will also become y plus 2 and y minus y2, y minus 5 is equals to 0. This will be the equation of the circle. Okay. Now, some people can say like I will consider this BD as the diameter. You can do that also. Considering BD as diameter, if you consider BD as diameter, right? So, what will be the equation of the circle? The equation of circle will be x minus 4, x minus x1, x minus x2 plus y minus y1 means x plus 2 and y minus y2, y minus 5 is equals to 0. So, if you observe, both these equations will be same, x minus 4 into x plus 2 plus y plus 2 into y minus 5. So, you can simplify this and get the answer. I am living here only. So, anyway, whether you consider AC as diameter or BD as diameter, you are going to have the same answer. So, this is question number 16. It is saying that the find the equation of circle which passes through point 1, 1, 2, 2 and whose radius is 4, 1. Okay. So, it's saying it is passing through 2 points. So, let me take it as A, 1, 1 and this is B, which is 2, 2 and we know the radius of this circle. We know the radius of this circle as 1. Okay. So, 3 informations are given. There's 2 points and 1 radius. Now, we have to derive the equation of the circle. So, let me write the equation of circle in the center radius form like this, x minus h whole square plus y minus k whole square is equal to r square. Where c is the center of this circle having coordinates as h comma k. We can write this standard form of circle in this way also where the centers in center radius form like h and k is the coordinate of center. And r is the radius of the circle. Now, this 1 comma 1 and 2 comma 2 must satisfy this equation. So, 1 minus h whole square plus 1 minus k whole square is equal to what is r? r is 1 means that is equal to 1.   Now, b should also satisfy this equation. So, putting that also 2 minus h whole square plus 2 minus k whole square is equals to 1.  That will be equal to 4h square plus k square minus 4h minus 4k plus 4 plus 4h minus 1 that will be 7 plus 7 is equals to 0. Now, comparing these two, this 1 and 2, they both represent the same thing. So, we can say this minus 2h minus 2k plus 1 is equals to minus 4h minus 4k plus 7. So, this will become 2h 4h minus 2h 2h 4k minus 2k plus 2k and 7 minus 1 that will be 6. So, h plus k is equals to 3. We got this relation h plus k equals to 3. Now, putting this in any of the equation, what we get? Let me put it in this equation. I will be getting 1. So, what will be h? H will be nothing but 3 minus k. So, putting h equal to 3 minus k, I will get 1 minus h, 1 minus h.  So, it will give a quadratic, right? It will give a quadratic in k.  So, this will be k square plus 4 minus 4k.  So, this will be 2k square minus 6k, 2k square minus 6k. This plus 1 minus 1 will be cancelled. Plus 4 equal to 0 or k square minus 3k plus 2 is equals to 0.  From here, we get two values of k. k is equals to 1 or 2, okay? So, putting k equal to 1, if you say, when we put k equal to 1, what will our h be? Our h will become 3 minus 1, that is 2. And if when k is equals to 2, our h will become 1, okay? So, when k is 2, h is 2 and when k is 1, h is 2 and when k is 2, h is 1.  So, let me put h is 2. So, this will become x minus 2 whole square plus y minus, when h is 2, k is 1. y minus 1 square is equal to 1. This will be our one first equation. And when we consider h as 1, I will get x minus 1 whole square. In that case, k will be 2. So, y minus 2 whole square is equals to 1. So, this is the second equation. So, both are our answer, right? So, this both will be our answer, okay? This will be also, this will be also our answer. So, moving ahead, this is our last question of this exercise, exercise number 2. So, it is saying that find the equation of circle, which passes through the points 3 comma 4, comma 3 comma minus 6 and 1 comma 2, okay? So, through three non-colonial points, only one end, one circle can pass, right? Through two points, infinite number of circles can pass, but through three non-colonial points, only one circle can pass. So, let me consider the equation of circle as our standard equation, that is x square plus y square plus 2 gx plus 2 fy plus c equals to 0. Let me consider this as the equation of the circle. Now, since it passes through all these points, it must satisfy all these, means all these three points must satisfy this equation. So, sorry. So, let's put it, it will be 9 plus, I am putting 3 comma 4. So, 9 plus 16 plus 2 into 3 6 g, 6 g plus 8 f plus c is equals to 0, right? So, further we can simplify it. So, this will be 6 g plus 8 f plus c equals to 69 minus 25. So, let me put it as equation one. And that second point will also satisfy it. So, this will be 9 plus 36 plus 2 g into 3, that is nothing but 6 g. And 2 y means minus 12 f, minus 12 f plus c is equals to 0. So, this will be 6 g minus 12 f plus c, 6 g minus 12 f plus c is equals to 36 and 9 is 45. 36 plus 10, 46, 45. So, that will be minus 45. So, let's consider it as equation two. And this third point will also satisfy this equation. So, 1 plus 4 plus 2 g, 2 f into 2, that will be 4 f, 4 f plus c is equals to 0.  So, this is our three equations and we are having g f and c unknowns, g f and c as unknowns and we are having three equations. So, we can solve it. So, let me subtract this second from first. We will get 8 f minus. So, this will become 20 f, c and c will be cancelled out. So, 20 f will be equal to minus 25 plus 45, right? So, 45 minus 25 will be 20. So, f will become 1, okay? f will be equal to 1 and we can subtract this also. Or let me simplify it. That will become 6 g minus 12 plus c equals to minus 45. Or 6 g plus c will be equals to minus 33.  So, 2 g plus c equals to minus 9. So, 2 g plus c equals to minus 9. Now, subtract it. Subtracting we get 4 g. If you subtract it, what you will get? 6 g minus 2 g that will be 4 g minus 33 plus 9. That will be minus 24, right? So, g will be minus 6. And what will be c? If g will be minus 6, then it will be minus 12 plus 6 is equals to minus 9. That means c is equals to 12 minus 9, that is 3.  That is nothing but x square plus y square minus 12 x plus 2 y plus 3 equals to 0. This is the required equation of the circle. So, we are done with this exercise. We are done with this exercise. Okay. I think this exercise is clear to everyone. So, this is all for today. And we will meet soon with our next exercise, that is exercise number 3 of the circle. So, till then, take care. Tata, goodbye. Okay.


The X-Saber 3 is rather small and yet remarkable heavy. Not only in weight but also in features. It offers Roon endpoint, DNA rendering, Spotify Connect, MQA, DSD 512, a linear power supply, remote control and so on. The X-Saber 3 is to be connected to analog line inputs on your amplifier, like CD or aux using either XLR or RCA cables. The amp needs to be connected to a pair of loudspeakers or headphones. If your computer holds your music, you need a bit perfect music player software, like Amara or Ivana, J River Media Center or Roon. The computer then is connected to the DAC over USB cable. Or if you want the computer placed elsewhere, you can connect it to your network and use the DNA or Roon loud protocol to send the music over the network to the X-Saber 3. You control your music player software then using a tablet or a smartphone. For Spotify Connect or Tidal Connect, you use the Spotify or Tidal Connect app on your phone and link it to the DAC. Since the X-Saber 3 has several digital inputs, you can also connect other digital sources like a CD player, game console and TV. The X-Saber 3 itself can be controlled from the front or over the remote control that comes with the unit. The compact cabinet is totally made of black or silver anodized aluminium, with a top of tempered glass. It measures 310 x 218 x 43 mm and weighs only 3.5 kg. The front holds a glass strip that, when switched on, shows a series of touch sensitive backlit buttons and a small color display. To start left we see the standby button, a button to dim the backlight of the buttons, the input select button, a mute button, the display, the filter selector, the button for sync mode and the button for the setup menu. Completely right the infrared sensor. The up and down buttons on both sides of the display function in several modes. Normally they are the volume control but they are also used in the input menu and setup menu. The rear is rather crowded with, on the right, the IC mains inlet with next to it the trigger input and output that facilitates automatic standby switching in conjunction with other devices. Then the Ethernet socket and the digital inputs, USB audio class 2, transformer decoupled spidive, toss link and I2S on HDMI. This I2S input, by the way, is not compatible with the HDMI connections on your video equipment and is for connecting digital sources that have an I2S output on HDMI connector. Then on the left the analog outputs. Two balanced outputs on XLR and two single ended outputs on RCA. To open the XSaber 3 the bottom plate has to be removed. This cannot be done without breaking the warranty seal and thus the warranty. The top and sides of the chassis are machined from a slab of aluminium as Apple does for their laptops and for instance air acoustics for their top of the line amps. This produces an extremely rigid chassis with integrated shields between the power supply, digital electronics and analog electronics. On the left we see a 33VA Noratel UK to ROIDAL transformer that is connected to the mains inlet over a 150-230 volts voltage selector. The secondary side is connected to an isolated part of the circuit board that holds the rectifiers and buffer capacitors. Note the separation between this part of the PCB and the part below. That part holds the digital audio electronics and, on a piggyback PCB, the WiFi radios. This side of the PCB again is galvanic-y separated from the right part. The connection between the two is over galvanic isolators, both on this side and on the flip side. It brings a digital audio signal to this part of the PCB where the DA conversion takes place. From here the analog signal goes to this part where the analog circuits are. When we look at the flip side of the board we see the rectifiers and the 16 NishiCon 1000 microfarad capacitors for buffering. On the input side the Ethernet connector with the Realtek interface chip. The SPDIF input is transformer decoupled and has a TOSLink input next to it. The I2S input is directly to the left of it. The number crunching is done by an XMOS microprocessor that probably does the interfacing and exiling Spartan that might do the filtering and MQA processing. Like on the other side of the board here galvanic separators to avoid a dirty ground pain on the audio side. The ESS9038 Pro DAC chip does the digital to analog conversion with next to it the Loface Crystek CCHD950 series clock crystal. It is remarkable that the ESS chip rests against a protruded aluminium support in the chassis. From the DAC chip the analog audio is sent to both the balanced output stages ending in XLRs and the single ended ones ending in RCA. I don't like to talk much about the measurements I always do since the relation between the measurements and the sound quality are very hard to establish. In this case I would like to mention that the measurements show an extremely clean result with noise, distortion and linearity showing very low figures. The output voltage on the XLRs is 4.9 volts and half of that on RCA's. That is slightly higher than Redbook specs but will cause no problem. Given the size of the XSaber 3, the user interface is very clever but also a bit fiddly. But the infrared remote makes the use of the controls on the front only necessary on setup. Choosing an input is a matter of pressing the input selection button on the remote until the wanted input is shown in the display. Or use the input button on the front combined with the left or right button. All kinds of settings can be made in the setup menu, like for instance whether you want to use a cable network or Wi-Fi. For these settings you need to be directly in front of the DAC to be able to read the small characters in the display. The settings you might want to change during normal use, like input or filter type, all have direct access buttons on both the front and the remote. The selection of the 7 filter settings the ESS DAC chip offers can be done from the front or over the remote control. The display shows numerically which of the 7 filters is selected but which filter is behind what number is not documented. If MQA files are played, the only option is the MQA filter since that is fully compensating for the DAC's time smearing. Another interesting feature is the sync mode that lets you select between synchronous and asynchronous feeding the DAC chip. If the digital source has a very good clock, you select synchronous. If not, you let the internal clock take over which is effectively reclocking. This of course does not work over the network since that is asynchronously by nature. All popular audio formats are accepted up to 768 kHz PCM, MQA 384 or DSD 512 over the I2S and USB inputs and up to 192 kHz PCM and DSD 64 over SPDIF and TOSLink. The X-Saber 3 was connected to the Air Acoustic AX5-20 amplifier that drives the PMC FACT-12 signature loudspeakers on I2S-2 isolators over AudioQuest Robinhood 0 loudspeaker cable. On the other side the X-Saber 3 was connected to the internet over an SOtM SNH10G network switch over an AudioQuest Diamond Ethernet cable that was in turn connected to my router. The X-Saber sounds very open, has very good detail and deep lows, very high resolution mids and fairly clean highs, all within the price bracket of course. The spatial information is what to be expected in this price range with more width than depth and fair focusing. Timing is rather good while sibilance is well controlled. This is a very good sounding DAC for the money that surpasses my reference in my setup 1B, the MiTech Brooklyn with Firm Hipsus and LOUSBREED signature. Although the Brooklyn also has analog inputs, even for phono. The X-Saber 3 is very well designed and built. It is versatile in accepting popular physical inputs, USB Audio Class 2, SPDIF, TOSLINK and I2S and it accepts several streaming sources over the network, Airplay, Tidal Connect, Spotify Connect, DNLA UP&P AV and RoonRoute. I like the compactness while it does have an inbuilt linear power supply. Since there is a built-in volume control, you can use it as a digital pre-app. This is a very attractive DAC for the € 3000 it costs. This brings us to the end of this video. As usual there will be a new video next Friday at 5pm CET. If you don't want to miss that, subscribe to my channel or follow me on the social media so you will be informed when new videos are out. Help me reach even more people by giving this video a thumb up or a link to the video in the social media. It is much appreciated. Many thanks to those viewers that support this channel financially. It keeps me independent and lets me improve the channel further. If that makes you feel like supporting my work too, the links are in the comments below this video on YouTube. I am Hans Beekhuyzen, thank you for watching and see you in the next show or on theHBproject.com. And whatever you do, enjoy the music.


All right. Hello, everyone. It's picking me up, right? Yeah, good. Hi, my name is Dan Willent from VMware. Appreciate you all taking the time to come to this session. I'm going to be talking, this is going to be mostly an overview session about OpenStack and VMware for people who kind of probably don't have a whole lot of background on that topic. We've got a bunch of deep dive sessions later here at the summit that I'll end with a slide that talks about all of those. So it's kind of where can you go next to learn more things. So a little bit about me. A background in networking and security. I joined a company, a startup, called NYSERA. I was there for a while, and as part of that was involved in the very early days of OpenStack, helped create the OpenStack networking project, which was then called Quantum, now called Neutron. And so I was the project team leader, PTL, for that for a couple years. And now I'm at VMware. I acquired NYSERA a couple years ago. And I head up our overall product and strategy around OpenStack. So it's kind of funny, I've been to every OpenStack summit now, since the first one, the private one in Austin. It's kind of helped me realize every six months, it's kind of like this drumbeat of, where is OpenStack now? How is it different from where we were a year ago, two years ago, three years ago? And so as part of that, I kind of started thinking, and kind of made me realize that OpenStack's gone through a couple different ages. And so everyone would probably have a slightly different definition of that, but this is kind of how I think of it. Like in the early days, it was fun. We stayed up all night, we hacked, we drank a little bit of beer, we hacked some more. It was all this kind of like, just grow the community, more people, let's get involved, hey, let's do this thing, it's fun. And this is kind of this age of formation, and there wasn't a lot of companies or vendors, necessarily at that point, vying for anything. Let's make this happen, let's take on the world. And then things like, I remember when I stepped in the San Francisco summit, I was like, where did all these people come from? And then like each summit, it was just more people, and more people, and more people. And it kind of, OpenStack and the expectations for OpenStack just kind of went through the roof. And in a lot of ways, I've talked with a lot of the early leaders of OpenStack about this, and in a lot of ways, there's this notion of kind of like OpenStack was something for nothing. It was a cloud for free, it was amazing, it was this opportunity, and everyone was kind of piling in to figure out what was going on. In fact, someone used a great analogy, this isn't mine, I don't know if he wants me to give him credit, so I'll use it generically. But he said, people kind of had this impression that OpenStack was like my sequel. It was just something you downloaded, you installed, and it worked, and then you moved on to the next thing. So I think that really kind of inflated these expectations around OpenStack that in some ways were actually very hard for OpenStack to measure up to and to deliver on. And so my theory now, and obviously anytime you're, it's easy to look back three years ago and say where you are, it's always harder to make statements about where we are today. But I kind of see us now moving into this age of more pragmatism around OpenStack. People kind of understand what it is better, they understand what it's going to do. And their main question is kind of, how does OpenStack drive value for my business? It's not so much, wow, there's this cool thing that I like to hack on, it's not that, oh, it's this amazing thing for free, it's hey, there's value here, how does that value apply to my business? So if you look into what's caused this shift, it's an interesting question to ask. I think in part it's just more awareness of people who've actually used OpenStack. People have now downloaded it, they've stood it up, they're not just reading articles about it, they actually have firsthand experience about it. There's also this great operator meetups now where you can hear stories from everyone else, people have a much more realistic view of what it means to use OpenStack. And that it's not something that you just download like MySQL and are off to the races. But it's also, my theory at least, is that it's also I think a changing set of people looking at OpenStack. And people who are not these web-scale companies who are gonna throw a bunch of developers at it, but they're actually enterprises saying, okay, I have my existing technologies, I have my existing teams, how is this going to work for me? How does OpenStack help my business? And so there's a handful of general directions or general shifts that I've seen. The first and probably most obvious one is a shift from this free do-it-yourself model more to using some vendor to de-risk. Even some of the very earliest people who are all gung-ho about I need to tweak this part of OpenStack and this part of OpenStack, once they've gone through a couple upgrades, this and that, they're kind of saying, maybe I don't need to tweak this, maybe I'm just going to have someone else help me with that. Another one is kind of early days, everyone's like, oh, I'm gonna hire a bunch of OpenStack-enabled developers and they're gonna come on board and I'm gonna have my cloud project up in three months. Suddenly realize, well, everyone else is trying to hire those, you know, there's 20 of those people in the world and everyone was trying to hire 20 of them. So it's much more of a shift now to, well, how do I take my, how do I enable my current team to deliver OpenStack, as opposed to assuming I'm gonna hire this new team that's just out there. And finally, and this is something that probably is pretty consistent that you're hearing across talks and at the keynote, it's all about from a focus on kind of, oh, this is free or this is cool technology to how do I enable developer innovation? And so let's go into, you know, that's the most important point here, I think, and ultimately that's kind of, my takeaway of this whole kind of thought experiment was that really I think this age of pragmatism is really about people separating out the why of OpenStack from the how of OpenStack, which was something that's actually very surprisingly, it seems obvious now, but it's surprisingly very muddled early on. You know, the why is pretty obvious. There are businesses that want, that see software as a key differentiator, right, and they see automation via APIs as a way that help their software development teams, you know, deliver software faster and more reliably, because they can repeatedly deploy through dev, test, and production. And OpenStack's the house side of that. OpenStack's a framework, right, that enables those APIs for automation. And importantly, you know, it enables those APIs on top of your choice of underlying infrastructure. So that's kind of the context the rest of the talk will actually be talking specifically about VMware. But I actually think this shift in focus is actually important, because these are the types of discussions that we like to have with our customers around OpenStack. It's not just, you know, great, supports OpenStack APIs. Well, any way you run OpenStack is going to support those same standard open vendor-neutral APIs. The real question is, what technology do I pick as an engine? You know, that gives me the operations capabilities I need, the security I need, the ability to troubleshoot, the ability to scale, et cetera. And obviously I'm from VMware, and I think we've got some really cool technology on that front. And so that's what we'll be talking about for most of the rest of the talk. So, you know, the high level way that we think about the value of OpenStack in VMware for our customers is, again, developers should only ever have to deal with those open vendor-neutral, you know, standard APIs that let them innovate, right? But the person running the cloud, the person, you know, in the old days, I'd say carrying a beeper. I don't know what, you know, maybe it's a cell phone now or a smartphone now. But, you know, it's what tools do they have, right, to reliably, securely deliver a cloud infrastructure, you know, based on their existing skill set and existing capabilities. And that's really where the value of bringing the OpenStack APIs and the rock solid VMware infrastructure comes together. And really, I think of this as an opportunity in several ways.  It's a way for them to say those cloud developers can use all the tools, they can use the OpenStack APIs, the CLIs, they can use heat, they can use horizon, et cetera, right, but they can do that in a way that works with their existing ops team. Those existing ops teams continue to use their same tools, the scripts they have built, the third-party tools they have brought along, all of their existing knowledge and expertise. So, you know, it was really great. We actually worked with the OpenStack foundation. The foundation came to us and said we want to write a white paper about how OpenStack can be accelerated into the enterprise using OpenStack on top of VMware. And so, we actually, you know, they had one of their staff writers work and they actually put out this white paper, they talked to several customers who are using OpenStack in VMware. And so, this was a great example of why I think actually running OpenStack on VMware is a fantastic opportunity for the OpenStack community as a whole, right, it makes it easier to make this technology, you know, be accepted and be embraced and have enterprises take it and run with it. But of course, I actually think OpenStack is a great opportunity for VMware as well, right. Ultimately, as VMware, the way we look at OpenStack is that it's a set of APIs and tools and layers, right, that can make our core product much more attractive to this new generation of developers who wants everything to be API-driven. And so, what you can see up here is a picture of that's our CEO, Pat Gelsinger, up at a stage where we have a VMworld room slightly larger than this, I'd say about 30,000 people in there, right. Telling, you know, maybe a little I'm just estimating here, but, you know, telling, you know, all the 30,000 people there and all the people watching the live stream how VMware is making it easy for VMware customers to consume OpenStack. So this is a product that we announced last at VMworld, it's called VMware Integrated OpenStack. Launched as a beta at VMworld just went GA about two months ago. And, you know, our goal here is if you've already invested in vSphere, right, VIO is free to use. And if you want to pay us for support you can pay us just 200 bucks a CPU per year. So our goal here is to make it both from a financial perspective and from a needs of use perspective very easy for anyone who knows how to run production grade VMware infrastructure to use that to deliver OpenStack to their development teams. So it's always very exciting when you see your boss way up on the stage talking about your product. So that's why I always like that picture. So, hopefully that makes sense at a high level. I'm going to step back a little bit and provide a little context next. So, you know, I mentioned I came to VMware through an acquisition of NICERA. NICERA is actually a company that started out, we actually created OpenFlow, we created the first OpenFlow specs. We created a project called OpenVswitch which, you know, is an open source virtual switch that's still actually at the heart of most OpenStack networking whether you're using VMware or not. And so, you know, pretty soon after we started OpenVswitch, NASA and Rackspace created OpenStack and because of our involvement with OpenVswitch and because Rackspace was using the NICERA technology, they invited us to be part of OpenStack and from there, you know, NICERA was primarily involved in the networking project which is now called Neutron. Once the acquisition happened and NICERA joined VMware, basically VMware had a choice. A lot of people said, oh, VMware acquired NICERA, now they're going to shut down all that OpenStack stuff that the NICERA team did. But actually, you know, we had a lot of discussions about it and VMware was actually very open and they said, actually, we're going to double down on OpenStack. We're not just going to keep the NICERA stuff integrated with OpenStack, the whole rest of our product portfolio with OpenStack. And so what you can see is over time, we've integrated with Nova and Cinder and Glance and Solometer and now we've even launched a full GA product to deliver OpenStack to our customers. So again, this is about VMware's commitment to open APIs, open interfaces for our customer and contributions to the open source community. I want to provide a quick update on a couple of things around Kilo. So obviously, you know, in terms of upstream involvement in OpenStack, we're kind of regularly one of the top 10 contributors to OpenStack, you know, in the Nova, Neutron, Cinder, Glance, all those core projects. And the fact that we upstream this code means that you can download the open source OpenStack code and run it with VMware products. You can actually go to a third-party vendor like Canonical or Red Hat or Morantis or HP and use their distros or NSX technology. And so, there's a lot of options in terms of how you can run OpenStack on VMware. It's not just VMware integrated OpenStack. Another thing to call out, I mentioned earlier, we've been driving the OpenVswitch project for quite a while. We also, just recently, earlier this year announced something called OVN. It's basically, it's kind of a add-on to the OpenVswitch project to solve a lot of the virtual networking challenges. OpenVswitch itself exists only on a particular hypervisor. OVN is about creating those together, creating virtual networks that overlay on top of individual hypervisors to provide virtual networks. So think of this as a base capability. It's compatible with KVM, compatible with Zen as well. And VMware and Red Hat are pretty much the main people. This is all open source. Keep an eye out. I think I heard something that there's a release coming up soon, but I don't know the exact date. So if you want to see the announcement, there's a blog post there, just Google OVN. That's really cool stuff. Another thing we've been driving with an OpenStack is something called the Congress Policy Project. So this is really about saying, well, there's all kinds of rules and policies and enforcement that an enterprise or other business is going to typically want to be able to do on top of OpenStack. And those things don't exist only in this project. They actually span projects. It may be that if you're booting off of this image, that means you can't connect to the network because this isn't a validated image. And so we helped create a community around this Congress project and actually just this last cycle, it was actually promoted to a full OpenStack part of the official OpenStack project. So that was a big win. You can see some of the other companies that are working with us on Congress as well. That's the result of all of this upstream work we've been doing and integration. Like I said, it's really about making sure that there's a great way to leverage every bit of the VMware technology stack if OpenStack is the way you want to think about your infrastructure. And so, you know, in the world of OpenStack, really, there's two main sets of people we think about. We think about the application development teams, right, the DevOps team. They're building their applications. They're either writing scripts against APIs or using some third-party tools like Vagrant or Chef or whatever to orchestrate the automation, the deployment, the upgrade, the scale out and scale down of their application. And all that application management and automation happens on top of the standard OpenStack APIs and tooling. And that happens with VMware integrated OpenStack or with any other version of OpenStack that you're using. And the question really comes down to this cloud infrastructure team. And what technology is the right set of technologies for them to be able to deliver a world-class cloud to their application development teams? Because we already said earlier, right, those application developers, that software they're writing is what's differentiating the business, right? We need to provide them with great cloud infrastructure so that they can move quickly and build great applications. And so, all the way from the virtualization technology to the hardware technology to the tools that you use to operate, manage and troubleshoot, monitor that infrastructure, those are all decisions made by the cloud infrastructure team. And this is, of course, where a lot of the VMware technology plugs in. So, for example, we've done integration with NOVA so that I can talk to vCenter and ESX. Probably the number one question we get here is, hey, do I still get to use things like vMotion and DRS when I'm using OpenStack with VMware? And the answer is, yes. We've done this integration in a way that OpenStack actually deploys to a cluster and so DRS can still move those workloads around where you can put a host in maintenance mode and it will evacuate. So, we've been very careful about how we've done that integration in a way to preserve a lot of the capabilities that people love about vCenter. NSX is a networking technology that actually is independent of vCenter or vSphere. You can deploy it with another hypervisor like KVM, you can deploy it with vCenter, you can deploy it with a mix of the two. But NSX lets you create virtual networks with no requirement about controlling the physical networking hardware underneath so you can create firewall rules and load balancing policies and isolated networks all virtually via API calls. From a storage perspective it's actually very interesting what we've done here. So, from both a Cinder storage and a Glant storage perspective we've integrated with the vSphere APIs for storage. And what that means is that any storage that works with vSphere automatically works with OpenStack and vSphere. That means whatever third party storage you're already using in your vSphere environment, all of that, no need for a particular Cinder driver or anything like that. It all just works. There's any combination of vendor storage that you have. It all just works out of the box. Because Cinder volumes end up as VMDKs on top of vSphere data stores. And that goes the same thing with VMware Virtual SAM, which we'll talk about a little bit later. It's a way to take the disks and flash in your hypervisor hard drives themselves and creates virtual storage area networks out of them. And so whatever storage or combinations of storage you leverage with vCenter you can automatically run that with OpenStack and vCenter. And this is actually very important because a lot of the value our customers see is that they can take the production grade infrastructure that they have today and they can immediately deliver OpenStack on top of it in a way that they can run at production grade. They don't have to re-evaluate or re-validate a bunch of hardware or new systems. In terms of operations and troubleshooting this is something we'll get into later. We have a lot of tools on that side that help you run a cloud better. vRealize is a suite of products. There's vRealize operations, vRealize log insight for log analysis and vRealize business for charge back. All of these have been integrated in a way that can play very nicely with OpenStack on top of VMware. And obviously you can run whatever you want at this higher layer because we're just exposing standard OpenStack APIs. But one of the products we also offer through our sister company Pivotal up at this layer is Pivotal Cloud Foundry which exposes a higher level platform as a service for your developers who want to build applications using that model. And then of course you can get OpenStack yourself, you can get OpenStack from a user to get OpenStack from VMware all in this tightly integrated package and that's called VMware Integrated OpenStack. So hopefully this gives you an idea. Like I said, there will be many follow-up sessions that will dive into specifically NSX and all these other areas. This is intended primarily to be an overview. So one thing that I always, you know, people kind of want to, a lot of times when people talk about running OpenStack in VMware, they're very focused on what does my application need, which is definitely one of the features of OpenStack. It doesn't need HA, it doesn't need different storage capabilities, etc. But, you know, it's also very important to say, you know, think about the gap between what you need to run a tiny POC on and the gap of what you need to run a production grade system on. So I've got a couple concrete examples. I don't know if anyone, this is one of my favorite blogs about OpenStack. I've used this for a couple years but it's still as true today as when they just from a guy who basically ran eBay's OpenStack cloud. OpenStack is a starting point for building a cloud. It's not a cloud solution. And there's a whole bunch of these other problems you're going to have to solve when you think about an OpenStack cloud. And that's ultimately where you have to think about actually, you know, consuming a solution or building your own solution. And that's a choice that OpenStack provides. So a couple concrete examples. So I mentioned that we use view-realized operations. We use view-realized operations. It's a tool many of our customers already use to manage their vSphere environments. And with view-realized operations we've added OpenStack intelligence to it. And that means two things. So first off, the OpenStack control plan itself, right? OpenStack, when deployed for scale with high availability is actually a pretty complicated application in and of itself. So we actually monitor that application. We can tell you if it's healthy and we can tell you if maybe one of your Nova API nodes is down or your Neutron API server is overloaded or it's lost connectivity to your vCenter, et cetera. All of those troubleshooting tools we can kind of automatically embed them into that interface. Secondly, if a customer calls up and says, oh, I'm tenant, you know, Foo on the OpenStack cloud, I'm having a problem with one of my VMs. You can actually pull up based on the OpenStack tenant name. So you can see all of their VMs using their OpenStack identifiers. And then you can see how they map from OpenStack VM to underlying vSphere VM to the physical server it's on, to the physical hardware it's on and the health of all those items along that path. So we'll be giving a full demo of this tomorrow. Very, very powerful stuff to see. Similarly, log insight. It's not just about log collection, which to be honest with you isn't that hard but it's really about the log analysis and being able to provide a bunch of very meaningful dashboards and alerts, et cetera.  We run OpenStack internally for our own developer consumption. And so we've taken a lot of that learning and mindset and built them into these two operational tools. There's also, I just actually found this while Googling around the other. This is another, this is one of their own experiences using Vrealize log insight to solve. They talk about how they install, they talk about how they actually had a real issue in their environment and did some troubleshooting there. So I thought that was always like real-world customer examples. So that was interesting. This is another thing, so actually both of these are examples of using NSX. This was a customer who, you know, wrote a post about how they were doing some cool networking with NSX across data centers. But the real thing is, lots of different OpenStack solutions can let you do a demo that you create a network here, create a network there. What I really like about that picture on the right is that that's actually, so you guys have all seen the topology view in Horizon, right? This is what it looks like when you've got, you know, a network or two networks. This is actually what it looks like when you've got, like, I had to trim it, but I think there are about 1,000 networks in that setup, right? This is what happens when you're actually using OpenStack for something like CI, you don't have one network, you don't have two networks, you actually get hundreds and thousands of these things. And so that's really, you know, the advantage of NSX. It's in, you know, you have to think about how is this system going to operate at scale? What resilience properties does it happen if one of my gateway nodes fails, right? Or what happens when I upgrade? Do all my VM users lose networking connectivity? If so, they're not going to be very happy. So NSX has solved a lot of those key issues from upgrade to operations to troubleshooting. And it's actually now, I think, this was actually a couple months ago. There's over 400 customers running NSX or leveraging NSX right now. So that's very powerful, very very powerful and actually hypervisor agnostic tool. So you can run it with vSphere, you can run it with any hypervisor as well. So this is a good one. I think the VMware security team may kill me for that. So how many of you have heard about Venom? If you're running a KVM or a ZenCloud, I really hope you heard about Venom. It actually doesn't apply to VMware, but I'm going to use it generically here anyway. It's a super scary security bug that was discovered very recently. Basically it means that someone who's inside of VM and should be isolated from everyone else can actually break out into that hypervisor and potentially break into any of the other VMs on the server. And depending on the security at your hypervisor layer could break into other hypervisors as well. So very scary bug. You can't patch this one soon enough kind of bug. But if you think about if you're a standard cloud, what are you going to do? Are you just going to immediately take down all your tenant VMs? Probably not. People talk a pretty big game about all my VMs, all my apps are cloud native. I'll tell you, even GCE for example doesn't just take down all your VMs, even Amazon sends you an email and kind of gives you some time to manage it. GCE actually has its own live migration capability now built in to help avoid these reboots. So even these more modern applications care about this type of stuff. And so this is actually something that's borderline trivial in a VMware environment. We have a combination of maintenance mode which evacuates servers combined with something called the VMware Update Manager which can automate the rolling patching of those servers. So this is just another example. Probably not the first thing you thought of when you were thinking about what platform do I choose for OpenStack, but a very important one that affects very fundamental security properties of that system. And again I'm just going to state for the record, this was not a vulnerability in ESX. Just kidding. For my own legal protection I'm saying that. Another cool thing, storage is another thing in OpenStack. It's easy to just think, well, any storage works in VMO, right? But then you have to think about, well how am I going to tier my storage? What different offerings am I going to have? So with OpenStack and VMware you have something called storage policies. Makes it very easy to create different tiers of your storage. Maybe my databases need lots of IOPS. Maybe this other thing is just for logs, so who cares. I just want cheap storage, etc. And so as I mentioned, any storage that works with vSphere or OpenStack and vSphere, this slide in particular is diving into VMware VirtualSan, which is kind of on this trend toward commodity storage where you can actually take disks and flash that exist in the hypervisor. And you don't have to manage a separate storage subsystem. It will actually aggregate them and let you give basically different levels of performance guarantees on a per workload or per disk basis. So you can, for example, I said you can have different tiers of storage. You can have a different type of storage, but you can also have a different type of storage. So I'm going to talk about the top numbers that have come out of here. We're talking over the 64 node cluster that's now supported in vSphere 6, you can get millions of IOPS even in well-tp mixes. The top number is just kind of random read. The bottom is a mix of I think it's about 70-30 read-write. You can get some of those as well. So that's a pretty big deal. So you can choose a hybrid mix of spinning and flash, or you can choose all flash. And, you know, as I mentioned this is all managed from vSphere in a way that's integrated with all those ops tools that I showed you before, makes it a very simple, cohesive system to manage and leverage. So, you know, just to go back, you know, I wanted to circle back and talk a bit about VMware integrated OpenStack. So everything I've said today, right, like I said, you could use VMware integrated OpenStack, or you can use VMware integrated OpenStack. You have to figure out what the right tradeoff is for you. I was just specifically talking about the VMware product, VMware integrated OpenStack. So what we do there is we basically take, you know, you take your existing vSphere environment, VMware integrated OpenStack is a combination of the upstream OpenStack code, right, with the VMware drivers enabled, and us having figured out a reference implementation of deploying the control plane, again this is all deployment. So we've got a lot of experience from a very practical experience with this stuff. With integrated tools for managing, installing, upgrading, how do you apply patches, how do you do rolling upgrades, how do you add a cluster after the fact, how do you add more compute capacity, date two things, all that integrated into a nice package that's very familiar to someone who runs a vSphere environment all day. And then, as I mentioned, integration and it's optional integration into these additional cloud management solutions. And then we wrap that all up in this validated architecture and we provide a single contact for support. And that single contact for support is actually probably more important than you might think. I mean, if you think about, you boot a VM, it fails to come up, it's in an error state. It's not at all immediately obvious, not immediately obvious and maybe after hours of looking at logs, right, was that problem actually in vCenter or maybe with their storage that's backing vCenter or maybe it was a problem with the Nova driver or the Nova scheduler, right. So having a single support contact there actually makes it much more fluid in terms of going from issue to resolution in terms of OpenStack. So, let me see how I'm doing on time. I'm gonna, yeah, let's do it. Let's see. So I'm gonna click out of here quickly and I'm gonna pop over and just, so there'll be a full demo of this. Like, tomorrow I'll show you, I just want to give you a little taste of of deploying VMware integrated OpenStack. So basically, again, the idea here is that any VMware admin this should be very, very familiar to.  So you can click on that and I click deploy OpenStack. It basically takes you through a wizard. Now, since I don't actually, you don't want to sit here watching me fumbling and type the whole time. I'm just gonna import a template here, which is one of the ways to deploy it, but I'll take you through each of the screens that you'd used to deploy in. Again, we'll go through this in more detail tomorrow. So this is really more just an example. So first off, I have to point to my vCenter, right? What vCenter am I gonna use to back this deployment? Then I'm gonna first pick a cluster where I want my VMs for my OpenStack control plane to be deployed to. These are my Nova servers and my Neutron servers, et cetera. So I just pick a cluster, use that. I'm gonna select the networking that I want to use for that cluster. So there's two network ranges. Configure where my load balancer is, right? Because this is a production-grade OpenStack cloud, you're gonna want a load balance for high availability and scale out. It's an inbuilt load balancer, so it's really, it's very simple to deploy. We just deploy it with everything else. Then I can pick one or more clusters that I want to add as my compute capacity, right? Where are the tenant VMs actually gonna land? Right? And then when they land, well, what data storage do I want them to consume their storage from? And we've made it very simple for Glance. Glance can actually just use a vSphere data store as a back-end as well. So you just pick what storage you want to use for that. Now for networking, we've got two different modes. You can use a basic VMware VDS that's built into vSphere, and you can use NSX for full-fledged neutron networking. In this example you see I've populated a couple things, describing how to connect to my NSX manager, what cluster of capacity I'm gonna use for my gateways. So I think in the same room after this is a whole deep dive on NSX, you'll understand what the gateway is by the end of that. Right? You know, for Keystone, right, where am I gonna get my users from? Either local database, or I can point to use LDAP to point to an server. Right? Optional can configure syslog, like a vRealize log insight, or any third-party syslog server. And that's it. So here's all my config, and I can just press finish, and this is sped up, depending on how fast your vSphere storage is, that we're cloning all these VMs onto. I've seen it as fast as about 15 minutes, and as slow as about, you know, 45 minutes well, maybe in a nested environment, or even a little slower than that, but basically it's all depends on, we're just creating VMs and cloning them. So you can see here, and then, you know, if you refresh, right? Nope, now I've got a running VIO instance, and if we click into that, you can see what we've done is we've automated the deployment of a fully integrated, full-scale out, highly available OpenStack control plane as VMs. And so at this point, right, you are more likely all of your cloud tenants, right, can then just use Horizon, or use whatever other tools they want in order to consume OpenStack capacity. Over time, you can add more vSphere clusters or more hosts to those clusters if you need more capacity. So again, very simple, very straightforward for a vSphere admin to deliver OpenStack services to their development teams, and that's really our goal. So just a couple more slides. You know, again, going back to that original core value prop that we talked about, right, it's about these open APIs that developers like on top of this really powerful, reliable OpenStack, sorry, VMware infrastructure that your IT operations team already knows how to run at production grade. And one of the cool things, I don't know, hopefully most of you are at the keynote, you heard about the interop stuff, but there's been a lot of fantastic work by the community to find these rules for OpenStack interoperability. What does it mean to implement the OpenStack APIs properly? So it's very fundamental to the core OpenStack vision. And so there's this thing called Defcore, and we've been very involved. We've got a guy named Mark Volcker from our team who's one of, you know, contributes a lot to that project. And so we're very proud to say, you know, on day one of this announcement, VMware integrated OpenStack is fully compliant in terms of the OpenStack interoperability requirements. And so this is a screenshot. If you go up to the, you know, the OpenStack marketplace you will see that little tested icon. What that means is we have proven through the battery of tests to show that we are fully interoperable from an OpenStack API perspective. That's very fundamental to the commitment VMware's making to our customers that we are implementing standard OpenStack APIs on top of our infrastructure. Not some VMware variant of OpenStack or anything like that. They're fully compliant with the OpenStack standard interoperability definition. So I'm very proud of our team and all the work they've put into not just building the product, but actually using that validation as well. So as I promised I'm going to wrap up. But this is our couple, I'm going to give you a couple slides of places where you can go to learn more. These are all the sessions at the OpenStack summit that are still to come that are related to VMware. How many of you were at the Adobe session just before? That was a great one. You just missed it. So Adobe is one of the early customers using VMware integrated OpenStack. I'd encourage you to go watch the video because that one already happened. So I can't tell you to go there. But we've got a set of sessions. Later today we've got NSX in this room. I think it's the same room. Yeah. And then tomorrow, basically mid-day, we have a set of three sessions in a row that we'll talk about. First it'll be a customer panel which I think I have a dedicated slide there. So it'll be Franz from Adobe again. It'll be Prashant from Wells Fargo and Peter from Nike talking about their experiences with OpenStack running on top of VMware. So I'd really encourage you to check that out. A couple other sessions that will be one deep dive demo that takes you through that whole installer and the operations experience as well. So that's a very powerful thing to see. And then, you know, for once you go home, this is where you go home to download it. So once you go home, you can download it. Like I said, any VMware customer can download and use this for free. It's available via the VMware website. If you want to come by, you can use both chat, ask questions. We can give you a full demo there as well, one-on-one. A couple other areas. So VMware has these things called hands-on labs, which are just amazing.  And you click a button in your browser. We spin up in our internal cloud and you can access and poke around and you're driving a real VMware integrated OpenStack installation. So that's available at any point. On that website, it's available. So it's very cool technology. Also starting, I think starting next week, there will be a three-hour, I think it's three-hour about full OpenStack training targeted for VMware administrators who want to get up to speed on OpenStack, learn more about OpenStack. And then there's a whole community that you can actually ask questions and it's a forum. And then obviously you can follow us, you can follow our blog, you can follow us on Twitter as well. I just wanted to wrap up. I just wanted to say we've got some snazzy. We've got OpenStack, Summit, Vancouver and VMware.  And with that, I'm happy to take some questions. Please use the microphone if you could. Thanks. Hi. Can you hear me? Yeah, thank you. And just if we are installation on this sphere and this center is all version 5, can we start using this or we have to... Version 5? Yeah. 5.5. Just 5? 5.5. So it's a 5.1, so yes you can. Oh, 5.5 you're golden, man. Yeah, you're good, you're good. So basically the question was what vSphere versions... General rules, if you're 6.0 or 5.5, you're golden, don't worry about it. If you're 5.1 or older, come talk to us. There are some ways that I can work with. There are also some caveats that I wouldn't want you to trip up on. Yep. I'm curious about where is vCloud in all the stuff that you mentioned? Should we consider it that? VCloud? Yeah. VCloud Director? Yeah. So vCloud Director actually is already a product that is no longer being offered to enterprise customers. That actually happened well before we announced VMware Integrated OpenStack. So what there is, is there something called VRealize Automation, right? Which is another kind of... I would say it's another kind of solution, more targeted at enterprise IT self-service. Whereas OpenStack is more the kind of the AWS style, very developer, API driven, driven type of a cloud. VCloud Director is still obviously used for our service provider partners though. But in terms of orchestration or automation, what VMware will push from...  You guys will offer OpenStack as the choice for orchestration or automation later. At the end of the day, cloud is a generic enough concept, there's not going to be one offering that's right for everyone. The key thing to realize about VMware Integrated OpenStack, right, as well, we have a set of customers who are interested in consuming their infrastructure via OpenStack APIs. We as VMware say, great, we want people to consume our infrastructure or however they see fit. VMware Integrated OpenStack is a way of enabling OpenStack consumption on top of our infrastructure. The same way we've created the Cloud Foundry product and we created a product and spun it out as pivotal way to consume our infrastructure as Cloud Foundry. We have products to make it easy to consume our infrastructure as Hadoop, et cetera. Particularly, I didn't mention this, but I don't know if any of you have seen the announcements around the container stuff, but VMware just announced two open source projects, one in Lightwave. I encourage you to check them out. This is my team as well, so I had to try to get a plug-in. But again, containers, great. We're embracing different ways of running containers and we've got to love to have discussions about our customers about why we think containers run best on top of VMware infrastructure. Any other questions? Cool. I appreciate it. Take care. Come up and get a hoodie.


Well, the chemical industry is a sort of bellwether industry. It's a very early indicator of what's happening in the world economy. We produce the basic building blocks from which everything else comes. And I think we've seen a great recovery since the downturn of 2008-9. And we're just seeing that coming off the boil now. We're just seeing things coming, slowing down. General demand is beginning to slow down. And that's really, I think, related to the troubles that are going on through Europe in terms of lack of confidence. So that's the issue that's around at the moment.


So what self-interest really means is not what we typically describe as following your emotions, doing whatever you want to do, being mean to other people, backstabbing, cheating, stealing, lying. All of that is bad for you. Can you ask me about that in a Q&A?  You'll discover that and you can try it out if you don't believe me. You know, take your best friend and spend the next week lying to them and see how long they stay your friend. They won't. Try it in business.  Stealing, cheating, all these are awful strategies if you want to live well. So if you want to live well, you want to use your mind.  And all of us are capable of that at some level. So self-interest is the pursuit of your own happiness, using your mind to figure out what's good for you in the long term. Now, if you hold that view, what kind of political economic system do you want to live under? Well, what you want to live under is a system that leaves you alone so you can think. What's the enemy of thought? What's the one thing that stops thinking? It freezes your mind.  Can you think? Can you do math? Can you build a bridge? You can't do anything. You're frozen because 2 plus 2 is not equal to 5. Force, coercion, authority, authority with a gun, those are the enemy of progress, of success, of your individual happiness because they're the enemy of human reason.  It's a society of freedom. It's a society of free markets. It's a society of capitalism. So the moral case for capitalism is the moral case for reason. It's the moral case for individual happiness. It's the moral case for freedom. Freedom and capitalism are synonyms in important ways.  You can't drink that soda. You can't consume this. You can't work for that wage. We're going to tell you how to run your life. Really? You think you know better than me what's good for me? When did that happen? Don't I have a brain? Don't I have a mind? Can I think for myself?  And I believe that morality on moral code should reflect that fact. So I'm a revolutionary. Not in politics, not in economics, but in morality. That's what we need to change. That's what we need to rethink. And that's what I think the real radical stuff is. We think our purpose of life. My purpose of my life is to live the best life that I can live for me. And by the way, that means I'm kind of nice to other people because they're important to me, right?  They do great things for you. All right. So if we want capitalism, if we want freedom, if we want to do well financially, if we want to do well materially, we need to rediscover new morality, a morality of self-interest. The old morality is compatible with socialism, death, destruction, and poverty. Thank you all.