Well, I think we're on time, and it's good to be with you. This is a little unusual format, because we want to do as much Q&A as possible. And so let me ask, is there somebody out there with microphones that can let participants ask questions? Okay, thanks. Let me tell you what I've got here. This is, again, a very large inflammatory topic, and especially over the last 15 years or so we've had to face as Catholics a barrage of negative reporting, and yet a lot of it necessary, because we, as a community, have not managed our affairs all that well. So let me say that here are some things I would like to, I'd like to give a very quick introduction to media, things that you really want to know about the way media works. So give you some idea of how stories are being reported. I'd like to give you one example of how I think we can turn the tables when stories that are reported that turn out to be bad news. And then I'd like to just ask you to bring up questions. Church and politics, the abuse scandal, dealing with physician-assisted suicide in euthanasia. Many people have questions about Pope Francis and how he sees himself as a media figure, and Pope's our media figures in our day and age. So this will be a little more conversational than my presentation this morning. But so keep these things in mind, and you can ask any questions. I just want you to know that what I'm especially prepared for are dealing with the question of the church and politics, Pope Francis, the abuse crisis, assisted suicide. I'll also talk about condoms and AIDS and the media in general. So have a lot to say. Let's jump to it. The first thing I think to keep in mind is that news is a manufactured product. It really is. We have to keep that in mind. We're dealing with commercial media here. They create a product, and media productions are really not done for their own sake. They are done in order to sell advertising. What you're really watching when you watch a news show is not the news. The news is simply the vehicle that they can sell advertising through, and we should keep that in mind, because as a commercial entity, that means their interests are not going to be catechetical, they're not going to be patriotic, they're not going to be apostolic or ministerial, it's not going to be academic. And in some sense it's not even about being political. Media and news is about arresting the attention of a particular market. They know who their audience is, they're trying to expand that audience, but they're also trying to please their base audience. They have it all categorized at different levels, and that is done for the purpose of selling advertising, and it's always been this way. That's not new. It's one of those things that, I mean I worked for a national broadcasting network at one time, and the owner of the network told me, Al if I could do it I'd run commercials full time. He was very upfront about it, because that's what it is. So that's the first thing to keep in mind. We're dealing with manufactured products here when we talk about the news. Really for a variety of reasons, the public significance of religion has receded in our lifetime. It's been going on for a long time, but it's been escalating in our lifetime. People are still religious, they still have faith, but they don't occupy the controlling positions or the creative positions in what we call the engines of modernity. We have Catholics and other Christians all over the place, but their faith is not able to control or be an especially creative force in media, in politics, in the academic world, in the entertainment world, in multinational business. We have people there, but none of those institutions are there in the name of the Lord Jesus Christ. At one time they were. At one time the New York Times was a great Christian newspaper. So not saying we should expect that to happen again, I'm just saying we are in a particular moment of history in which things are very secularized. And that word secular simply means that, let me say secularization is the social process by which religious ideas and influences and institutions are pushed to the sidelines of life. If you were to ask a number of great thinkers, American thinkers in 1860, what's our national purpose? The group that you would ask would probably have 50% of them would have been clergymen, and the rest of them would have been probably mostly Christians of some sort. You might have had a free thinker or two in there. By the turn of the century in 1900, the number of clergymen would have been reduced by at least half, and by 1950, in fact, there was a project like this in 1950, they asked a number of leading thinkers about America's national purpose. There was no theologian on the panel. They had an evangelist, Billy Graham, which is fine, but Billy Graham never saw himself and he was never considered to be a theologian who is going to deal with world ideas. That was in 1950. So we're living in a different period, and secularization by pushing religious influences and ideas and institutions to the sideline means that in the mainstream, in the center of things, many other interests vie to control. Commercial interests are there, political interests are there.  Here, I'll give you a good example of secularization here. It's a kind of a silly one, but I think it's actually a good one. When the Vancouver Winter Olympics were going on, Vice President Biden was there, and he appeared in public and he had gone to Ash Wednesday, and he had ashes on his head. Well, broadcasters in London on the Sky News Service were perplexed. They were saying, well, what's going on there? He's got some bruise on his head. Kay Burley says to her colleague, what's happened to his head? I'm sure that's what everybody's asking at home. It looks like he walked into a door. And so Burley and her co-anchor discussed the possibility that Biden may have slipped on the ice while he was in Vancouver for the Olympic Games. And then it dawns on her, oh no, I'm a very bad Catholic. I know today's Ash Wednesday and that those are ashes on his forehead. She mercifully had a break to go to, but think about that. A Catholic on Ash Wednesday in a major news media outlet sees the Vice President of the United States, and it never occurs to her, it's not on her radar, that he'd have ashes on his forehead. That's secularization. This religious meaning and significance of things are off on the side, not in the center. So we need to understand that news is a manufactured product. The second thing we want to understand about it is that news media like the little guy, beating the big guy. News reporters always dream of being a journalist who can make a difference. And usually that means that they find some victim or some little guy who's been abused by some oppressive institution. Right now that's our problem, to be honest with you. It's been set up so that the Catholic Church is now seen as a victimizer. Rather than an advocate for victims, we are largely seen as a victimizer. And that means that to satisfy their audience, they'll be looking for stories in which the Catholic Church looks like an oppressive institution that needs to get its comeuppance. And right now that's, we're living with it. The church is big. It's got a billion, more than a billion adherents, 17.5% of the population of the globe is Catholic. We've got 5,000 bishops. We've got almost a half a million priests, 41,000 married deacons. We've got 700,000 religious sisters. We've run more than 220,000 parishes, 5,000 hospitals, 7,500 dispensaries, 15,000 homes for the elderly along with tens of thousands of schools. We're probably the largest or nearly the largest aid and development organization in the world right now. We're big. And in fact, one of the things that journalists like to put across to people is that big institutions, it could be big politics, it could be big business, it could be big media even. But they want to be on the side of the little guy. And right now the Catholic church is not seen as helping the little guy. We're seen as a victim here. Also because of the process of secularization, because religious ideas, influences in institutions are not at the center of our discussion and debate, religion is not an especially good field for journalists. It used to be that that was kind of the low rung on the totem pole. The religion beat, the religion reporter, you didn't put your top guys there. Part of the reason is that religion is an intensely interior activity, prayer and contemplation don't make good news. There's not much there to talk about. And so when they do report on religion, they like topics which arrest people's attention. They like stories about religious leaders that have feet of clay, scandal sheet, they like that. They like to show that the church is struggling to come to grips with modern time. You know, look at this, nuns are using the internet. Oh my gosh, man bites dog.  They like stories about scholars who challenge religious beliefs. Occasionally, especially in local television, you'll find stories about how this particular church that maybe is new and is operating under a little bit of public suspicion. They like to run stories about, look, these people are very nice after all. These devout people that you've been suspicious of are actually look at them. They get along well with their neighbors. It's another form of story that they like. They also like stories about new translations of scripture because they sound funny. You all should know that those who operate in what's called elite media, that's the national media in D.C., in New York, Los Angeles, big cities, they are political liberals. They vote about 80% Democrat, about the same, are pro-choice, and it's been that way since the 1980s at least, which is when I became familiar with the surveys. And they're also not only liberal politically, they're liberal and social mores. This is not true necessarily with your local paper, your local television station, your local radio. I'm talking here about so-called elite media. So they're liberal and social mores as well. TV executives, there was a poll of TV executives, 85% of them thought that adultery was not a big deal. Same poll found out, excuse me, 50% of them said that adultery was not a big deal. They also did a survey of the American public. The American public, 85% of the American public, thought adultery was terrible. It was immoral, but 50% of TV executives, these are the people who are responsible for getting our television shows up there, they did not think adultery was a big moral problem. Now, we just had a celebration of the space flight, 50 years, the moon landing, Apollo 11. Did any of you see a story dealing with religion and NASA, religion and the landing on the moon, religion and the space program? I see a few hands. That's good, actually. The interesting thing is that the NASA program was full of Catholics and other Christians, Gene Kranz, who ran the Apollo 15 rescue, devout Catholic, prayed all the time, a good number of the astronauts, I never made a count, but I've heard anywhere from 35% to 50% were themselves quote devout Christians of some sort. There were a number of astronauts shared communion, the Eucharist, Catholic Eucharist in space, Tom Jones was one of them. So we had the reading of Genesis chapter one and the first Apollo eight when they were orbiting the moon, when they landed on the moon, Buzz Aldrin was supposed to read from the Gospel of John, but Madeleine Murray O'Hare had been running a campaign to sue NASA for violation of establishment of religion. And so they decided they were not going to broadcast Buzz Aldrin's reading. He was going to read the passage where Jesus says, I'm the vine, you are the branches, you know, they wouldn't let him, well, he did it, but they wouldn't broadcast it. They were living in fear of Madeleine Murray O'Hare. So those are things that you should be aware of. They are just part of the way media works. 50th anniversary, usually when we look at a 50th anniversary event, we think this is special. So we want to usually go beyond just the mechanics of the event. We want to go to its meaning and its significance. I think it's interesting that apart from my program, and I'm sure some other Catholic programs, I didn't hear or see a single media outlet dealing with the spirituality of the astronauts, the religious commitments. And yet, if you look, there's a wonderful book out, by the way, called To Touch the Face of God, it's by, what's his name? Yeah, very good. Just had him on. It looks at the NASA space program and the sacred and the profane in it. Very good book. So those are things, keep in mind about media. All right. Now this is about when good news turns bad. What do you do with it? Number one, and I can't stress this enough, don't run, don't shun it, use the moment. You can use these moments as great opportunities to help people see what the church is all about. We're going to talk about how that's the case. Many stories about the church actually end up using church teaching against the church. We'll go into that a little bit later. When the church is in the news, even if it's bad news, people are interested, they're curious. I was just at a family reunion and my sister-in-law came to me and asked me, what about, you know, what I hear going on with these bishops?  I mean, what you're hearing is that we have a whole bunch of men who don't seem to be able to live according to their beliefs very well. And I said, what's really interesting is that in spite of how flawed Catholic leaders have been and are. We have, for 2,000 years, been able to sustain completely consistent teaching. So you can't trust Catholics, but you can trust Catholic teaching. And that was the point that I was able to leave her with. She said, oh, I hadn't thought of that before. I enjoyed it. And I think that's what we want to do. We want to get to the place where when these negative things happen, we're not intimidated. Don't shun the opportunity. Don't run too. Know who you are. Catholics, the Catholic way of life has been an incredible blessing to the human race. Virtually every area of modern life can trace its origins back to Catholic concepts and ideas. We all have our own personal experience with the church and we have many good things we can say about it. But the world doesn't know so much of what's happened. St. Augustine, for instance, Bishop of Carthage. We think of him as a saint. We think of him as a bishop. What you don't know is that he's one of the most impressive figures of the ancient world, the world of late antiquity. He is the most prolific and the most respected writer. His confessions is considered the greatest memoir of the ancient world. It's considered the first great primer on the psychological individual. Before Augustine began to speak about his relationship with God, his personal encounter with God, that wasn't done. It's hard for us to imagine that because we live in a very personal confessional age.   They'll talk about things that their husband did to them that nobody should know in public, but this wasn't true in the ancient world. The Catholic Church's insistence on the rationality of God is recognized by virtually all historians of science as essential to the beginning of what we call the scientific enterprise. The Catholic emphasis on the dignity of the individual is considered to be essential for the development of individual rights. A recent book by Larry Sidentop, an Oxford historian called Inventing the Individual, goes over how the gospel influence world thinking so that the dignity of the individual came to be something that we thought should be protected. Again, you can go look over most areas of life. And if you look carefully enough, I mean, take astronomy, for instance. This is when you say science in the church, people say Galileo. It's crazy because the Galileo incident wasn't one of our best moments, but it wasn't very big. It was a minor blemish, given all the positive things we were doing. J. L. Heilbronn, who's a historian of astronomy, writes that the Catholic Church gave more financial aid and social support to the study of astronomy for over six centuries from the late Middle Ages into the Enlightenment than any other and probably all other institutions. We can look at law, architecture, education, sculpture, literature, medicine, and you're going to find the same things. The father of genetics was a Gregor Mendel, a monk, an abbot. Nicholas Steno, blessed Nicholas Steno, was called the father of stratigraphy. This is the necessary science that led to geology. The father of the Big Bang Theory is father of George LeMontre, a scientist. Catholics have played important roles in the development of most areas of modern life. I mean, even the UN Declaration of Human Rights was influenced by the Catholic philosopher Jacques Maraton. So we need to know ourselves. We need to know there's nothing to be ashamed of in being Catholic. There are shameful deeds that Catholics have performed, but there's nothing to be afraid of or ashamed of in being Catholic. So don't shun the moment. Know who you are and know who you're talking to. If you'll notice, most of what the church is criticized for is not being who she claims she is. The standards that are used to judge us are actually standards that we helped create. Those who are our critics are not primarily atheists. They're not primarily Buddhists. They're not even pagans. They're secularized Christians. They're operating with Christian values that they've forgotten the source of. The secularization of the Western world means that people abandon the church, but they don't necessarily abandon that many of the church's values that they grew up with.   That's a Catholic concern that they have. And people think that the ancient world had a high view of human life and the church just picked up on it. It's not true.  It was a very, the ancient world was a very disposable world when it came to people. Plato taught that a poor man whose sickness made him unable to work any longer should be left to die. Seneca wrote that we drown children who at birth are weak and abnormal.  That's ours, all right? The church worked on that. It comes out of the Catholic thought in a book called Daily Life in Ancient Rome. Jerome Carpapino states flatly that the butcheries of the arena, the gladiator shows, the butcheries of the arena were stopped at the command of Catholic emperors. The historian of morals, William Leckie, about two generations ago, said there's scarcely any single reform so important in the moral history of mankind that must, that can't but be attributed to the Catholic church. So again, what we're dealing with our critics are frequently dealing with secularized Christians. And then the last point I want to make on this is always remember that when the church says no, behind it is a much greater yes. We get accused of being focused on rules, legalistic things. We're interested in principles. That's a misunderstanding of the gospel. The Sabbath was made for man, not man for the Sabbath. And that's true with a lot of things, as Pope Francis says, the economy was made for man, not man for the economy. Human flourishing is what the Catholic church built into the Western consciousness as what we ought to be defending and protecting. So let me, those are just some general, some general thoughts. So what I'd like to do now is give you one quick example of how to approach a problem. You may have remembered this goes back to 2009. When Pope Benedict was on a flight to Cameroon and he was asked a question about the use of condoms to stop the spread of AIDS. And Der Spiegel, the Germany kind of the German equivalent of Time magazine reported on this on March 17th of 2009. The Vatican encourages sexual abstinence to fight the spread of AIDS. And Pope Benedict reiterated that stance. You can't resolve it with the distribution of condoms. He told reporters aboard the Alitalia flight to Cameroon. On the contrary, it increases the problems. However, this is not necessarily a view shared by all members of the clergy with some priests and nuns who work with those living with HIV AIDS, having questioned the church's stance about 22 million people in sub-Saharan Africa are infected with HIV, according to the United Nations. Medical workers advocate the use of condoms to stop the disease from spreading. Rebecca Hodes, Director of Policy, Communication and Research at the Treatment Action Campaign in South Africa, hit out at the Pope's words, saying that if he was serious about fighting HIV, he would promote wide access to condoms. Quote, his opposition to condoms conveys that religious dogma is more important to him than the lives of Africans. Hodes told the Associated Press on Tuesday. Notice what's happening here. Rebecca Hodes is telling us that she's more compassionate than Benedict the 16th. She's the one who's most interested in saving lives. He's the one thoughtlessly sacrificing innocent lives by his hard-hearted commitment to the rules. He's putting his irrational moral code ahead of saving lives. And of course, if that were true, that'd be terrible. This is what Jesus' argument was with the Pharisees. You know, they said that Jesus was more interested in healing on the Sabbath than complying with all the Sabbath regulations. So we're in a funny situation with a lot of this reporting. Rebecca Hodes is playing the role of Jesus against the Pope. Now, now this is actually part of a much larger war going on on the earth, an ideological war. And the question is who leads what community, what nation, what church, what people, what set of ideas best lead to human flourishing? That's the gold standard. What best leads to human life in, you know, abundant life? Is it democratic socialism? Is it global Catholicism? Is it American capitalism? Is it the scientific community? Who best leads to shalom? Who best leads to human flourishing? And the debate over AIDS and condoms is a proxy war. The deeper question is what comes first, rules and doctrines or human lives? It's the question Jesus faced. Was the Sabbath made for man or man for the Sabbath? So many Catholics, when faced with this thing, immediately start trying to defend the church's teaching. They defend, quote, the rules. They immediately want to talk about what's wrong with condoms. Big mistake. You need to ask the question, what makes for human flourishing? Is our way of doing this the wrong way? Are we killing people by not distributing condoms? This came up in a BBC interview that I did about that time. Mr. Cresta, don't you think that the Pope is missing the point? This isn't about the rules of his church, is it? It's about saving human lives, Catholic lives, non-Catholic lives, Protestants, atheists, those with tribal beliefs. Do you think human life is the most important value here? Yes, I do think that's the most important value here. So you think the Pope is wrong? No, not at all. But I'm no expert in what stops the spread of HIV, and you're no expert. And the Pope's actually no expert on the most effective way to stop the spread of HIV in Africa. So why don't we ask somebody who knows the AIDS epidemic in Africa better than probably anyone else? Dr. Edward C. Green, he's an agnostic scientist who's the author of five books, 250 peer-reviewed journal articles. He works with the AIDS Prevention Project at the Harvard Center for Population Development Studies. What does he say about the Pope's approach to this? Well, it just happened March 29th that year. He had a Washington Post column titled Condoms, HIV, AIDS in Africa. The Pope was right. The overreliance on condoms in Africa has led to an increase in the spread of AIDS. The same point was made by James Shelton from the US Agency for International Development. Condoms alone have limited impact on generalized populations. No country in Africa has yet turned back a generalized epidemic by means of condom distribution. The Catholic Church has no interest in imposing its way of life on people. Once you impose your way of life on people, you're no longer Catholic. To be Catholic means to have chosen freely to follow Jesus, to be his disciple. And we believe that human beings are made for God. God's the ultimate source of life and love. We don't want to impose. We want to propose a better way here, a way that's more effective in saving lives. And I know it seems counterintuitive to people, but the evidence was on Benedict's side. And unfortunately, and this is where you have to turn the table and stick the knife in, unfortunately, there are people out there that are allowing their prejudices and ideological and political assumptions to blind them to what can best save lives.  Who's, so I ask, who's letting ideology and rules getting in the way of saving lives, the Pope or those political and social liberals who have equated condom usage with an ideology of sexual freedom?  Was the Sabbath made for man or man for the Sabbath? Are you more committed to a piece of latex than you are to human life? Turned it right around. That's what we need to be training ourselves to do, and it can be done. We, what we need is we simply need to have ways of getting this information in our hands and, of course, with the internet and what we're trying to do at Ave Maria Radio and UW-Chinus trying to do. We're trying to make this kind of information available. I could go into more details on this, but I don't want to. But notice what happened there. They, Rebecca Hodes, is criticizing us using the church's standards. Human flourishing is what Jesus came to bring, eternal life. We should always keep that in mind. If for some reason we're not seeing human life flourishing through Catholic teaching, we need to ask ourselves if we've got it right. She thought we had it wrong. She's the one who was wrong. AIDS, the spread of HIV in Uganda was largely stopped because of the Catholic approach on this.  If you want to go into that, assisted suicide.  Let's take a few questions. How much time do we have, by the way? Okay, good. So we've got time. Well, I'm sorry. I cannot, those lights are making it difficult for me to see. What are topics that you would like to talk about? Right up front here. About the sexual abuse crisis. Cardinal Viganos writing has created conflict about Pope Francis. How in the world do we address this from a layperson standpoint? In my own parish, there has not been a drop-off of people attending. Not been a drop-off of people attending. This, the sexual abuse crisis, I don't, in the masses I've attended, I've not heard anything about it. However, this is all over. This Cardinal Viganos writing and then other people who defend him, including the bishop from the Diocese of Phoenix, which is where I'm from, says, oh, he's just an honest man and I don't have a reason to doubt him. That's my diocese. That's the bishop in my diocese. And I just don't know how to respond when people ask about it. Well, let's ask, let's clarify exactly what the question is. Yeah. No, no, no, I understand that this it's a mess. It's very difficult to deal with this topic because there is so much in so many problems and it's so inflammatory. Archbishop Viganos has made statements beginning last summer and he, in fact, is a man who had a favored position. He was papal nuncio. There's no reason to disbelieve him. There's no reason to write him off at all. Now, it is possible that, you know, some he has some details wrong because he doesn't know everything and he's made some claims which we'll be able to test as time goes on. His first announcement called for Pope Francis to resign. Now, hear me out on this. So what? So what? The former papal nuncio to the United States called on Pope Francis to resign. You don't see that kind of thing every day. But don't you think that's happened in the past? Sure, that kind of thing happens in church history all the time. It's what he said Pope Francis did that should give us concern. He claimed that Pope Francis was aware that Pope Benedict the 16th had put a ban on Theodore McCarrick's activities. Now, most of us actually have too high a view of the precision and the competence of the Vatican offices. More than one person has said that while Pope Benedict said that, and I think there's every reason to believe he did put a ban on McCarrick, telling him that he had to sit tight. He wasn't supposed to be traveling around. He was not to be in the public eye. I absolutely believe that Pope Benedict the 16th did that. And I also believe because of other things I've seen Pope Benedict do that he didn't follow through and make sure it happened. This is a that is a chronic problem in Catholic culture. I I have worked in the last year with as part of a small group of laypeople dealing with those who were victims of priestly sexual abuse, noncriminal abuse. We were dealing with adults who were victimized and we were trying to provide help so that these victims could go and confront the bishop face to face. So the bishop would know what happened to this fellow. In two particular instances, the bishop of Lansing met with our people and ended up revoked, looked at the evidence and revoked the faculties of two priests. He believed the victims in this. Now, in the course, you would say, wow, that's great. Yeah, but at the same time, the victims were not entirely satisfied because there were other things the bishop didn't do. In one with one victim, he said that the bishop had ignored a previous complaint of his so that when we brought this fellow there, this is a fellow's second time. Why didn't the bishop get it right the first time? Again, bishops change every few years, and this particular bishop said, I'd never seen that right now. The diocese of Lansing doesn't have any of its priestly files. They're sitting in the attorney general's office. Now, most of you would probably say to yourself, huh, in an age, a digitized age, we have a diocese that hasn't backed up its priest files. They're gone. The attorney general came and took all the files. So you have a high view of how these congregations and decasteries operate. I don't. I think there's a lot of incompetence and a lot of ignorance. They're very insular people. Oftentimes people in Rome are playing for a coveted position in another place. So we think I don't know a single businessman who would have tolerated what some of our bishops tolerated during this abuse scandal. In fact, what I'll do, let me give you one case, case study on this very quickly. It's the story that led the Boston Globe to its investigation. It's the story of John Gagan. He was in a particularly egregious offender. He soiled the bodies and souls of at least 130 boys and young men over three decades. First assigned 1962 to a parish. He was observed in 1962 bringing boys into his bedroom. He was reassigned in 1966, though he was let go. He lasted there only seven months. No reason was given for his departure at his next assignment. Gagan was caught molesting a boy and was sent to Seton Institute in Baltimore for treatment for his quote, pedophilia. It would turn out to be the first of at least five formal treatment therapies that would he do over his career. In the early seventies, he molested four boys. The church settled a lawsuit with the mom of the boys. He was reassigned and at the next parish, he molested seven boys to which he admitted in 1980 to an auxiliary bishop. Unbelievably, Gagan claimed at the time that he did not feel it was a serious pastoral problem. The bishop thought otherwise, thankfully, and placed him on sick leave. And then the ordinary from the archdiocese of Boston at that time was Cardinal Archbishop Umberto Medeiros. He insisted that Gagan undergo further psychoanalysis and psychotherapy. In February of 1981. Now Gagan returned to pastoral work at a new parish where he raped and followed the boy in 1982. He was turned in by parents who discovered that he had arranged to meet with one of their sons, who he had previously abused. And at the time, Gagan was in the company of another boy. They were going to an ice cream shop together. Molestation complaints continued. And in September of 1984, a new archbishop of Boston, Cardinal Bernard Law, removed Gagan from the parish. Yet, two months later, law assigned Gagan to a new parish where unbelievably he was put in charge of three youth groups, including altar boys. The following month, December, 1984, the auxiliary bishop in one of the auxiliaries in Boston, John Michael Darcy, blew the whistle and wrote to the ordinary, the diocese, Bernard Law, complaining about this assignment because Gagan has a history of homosexual involvement with young boys. But one of Gagan's therapists amazingly claimed that Gagan had fully recovered and no restrictions were needed. In 1986, new allegations of sexual abuse came in and he was treated now for the fourth time this time at the St. Luke Institute in Silver Springs, Maryland, where he was diagnosed with homosexual pedophilia. April 1989, auxiliary bishop Robert Joseph Banks ordered Gagan to leave the ministry the next month, May of 89, he was placed on sick leave. From August to November of that year, he went to the Institute of Living in Hartford, Connecticut, where officials recommended that he return to parish work. The auxiliary bishop bought because the report claimed that he had made only moderate improvements. But the next month, the Institute stated in a letter, the probability that he will act out again is quite low. So the bishop thought, well, okay, I've got the letter from this place, they say he's not likely to act again and they put him back in a parish. What happened? The church received another complaint. Gagan was grabbing the buttocks of a boy in a public pool. In 1991, he was prosecuted in molestation charges. He was not convicted until 2002, where he was sentenced to eight to 10 years in prison. In the time between 1991 and 2002, he had retired, was living in a residence for retired priests. And yet in 96, more allegations surfaced and he spent several more months in therapy at the South Down Institute in Ontario, Canada. That's what you're dealing with. Does that sound like a bunch of real competent, and we know what we're doing people? Not in my eyes. There were a number of problems our bishops had in this whole era and I just think we just have to look at this thing with clear eyes. They had a desire to preserve the church's good name so they're slow to make anything public too. They failed to understand the deceitfulness of these abusers. They did not understand that these abusers are narcissists. They lie. They're manipulative. That's how they survive. And you can see letters from bishops to Gagan, in fact. Dear Jack, we're sorry about you having to be put through this interrogation again. They appeared to be more interested in protecting Gagan than they were with the victims. They believed in the power of therapy. And it wasn't until I think the 1980s where therapists finally began to realize we can't do much with these guys. And the difficulty many victims have themselves in talking clearly and directly about their experiences. So a lot of times bishops were only getting fragmentary stories from the victims. There's actually relatively little evidence of deliberate concealment or evil. But, and let me qualify this, there's plenty of evidence of ignorance and incompetence and an extraordinary lack of transparency with laity. And these failures would have led up to this cover-up, what we call the cover-up. Incompetence, ignorance, clericalism, Church in Diocese of Lansing, St. Thomas the Apostle, this goes back to the late 80s. There was a very good up-and-coming priest there who all of a sudden disappeared. He was gone. He was replaced. Nobody ever knew what happened. The bishop, at that time, decided not to tell the people why this fellow was gone. We found out later, in the late 1980s, that fellow was gone. We found out later, years later, because he was returned to another parish, had the same problem, and he had a problem with women, all right? To me, this is crazy. I asked about this, and they said, well, we wanted to protect his privacy. I said, his privacy? You've made him a public person. You've made him the leader of this parish. He's the leader of the community here. He hears the confessions of people. He's supposed to be, you know, building intimacy, building, loving one another, serving one another, honoring one another. You owe it to the laity to tell us why he's not there. So I asked the bishop about that, and he said, well, I actually don't really remember what we did then. So you see what we're dealing with. There's all kinds of things that creep around, and that's what led the Boston Globe to do its work. And the Boston Globe did us a terrible favor. And so when you ask about Vigano, my response is, I hope he writes more. I hope he tells more. I hope he is able to follow through on some of this stuff. Nobody, I mean, apparently he's afraid for his life, and he can't, you know, nobody seems to know where he is. But this is something else I want to get across. I actually meant to say that at the very beginning, we are in a strange day in church history, never before have laypeople had so much access to information. And I find very good Catholics spending an inordinate amount of time following ecclesiastical news and story, whether it's scandal stuff, or just who's up and who's down at the Vatican, they are flooded with information that previous generations of Catholics never had and never worried about. Let me say this as clearly as I can because I'm in the middle, I mean, I'm with this stuff every day. There's nothing spiritual about following ecclesiastical news any more than it's spiritual following political news or sports news. The pursuit of information about the church is not a spiritual exercise. It might at its worst actually be a longing for gossip and calamity. So, that's, so when you say, what do I do about vegano, I would say relax. You don't have to say, the truth is you don't have to have an opinion. I mean, honestly, and I say that as one who has lots of opinions, there are times when you don't have to have an opinion. My opinion on vegano is that I hope he continues to write and I hope men in high positions will pick up on what he said and I'm hoping that there will be bishops who break ranks. You realize up to this point we don't have any bishops who are siding with engaged and passionate laity. They won't come out. I pointed this out to a theologian about three weeks ago in St. Louis and he said, well, bishops don't break ranks because they don't have any canonical authority to report on another bishop who's doing a bad thing. And I said, what do you mean they don't have canonical authority? They have human moral authority. If you see somebody doing something wrong as a baptized believer for heaven's sakes, you have moral authority to blow the whistle on the guy no matter who he is. And I think part of our problem is we have an overly deferential attitude towards clergy and the Episcopacy. And part of that is a reaction after the Second Vatican Council. There are lots of people, liberal in theology who are downplaying, you know, the sacramental side of the church. And so those of us who were really interested in defending the church ran to the defense of priests and we wanted to show real respect. Well, we should. We should show real respect. But we shouldn't allow our respect for priests to get in the way of telling the truth. And I'm waiting for these bishops. I don't know if it'll be Strickland from Tyler, Texas. I like Olmstead and Phoenix, okay? Alexander Sample in Portland, Paprocki. There are a lot of really good bishops out there. But I'm waiting for them to side, to be a voice for laity like yourselves who are frustrated by this monstrous situation that we're facing. But remember this. You want to be able to speak well of Jesus and his church. Spend your time working on the wine. And don't worry that much about the wineskins. You will not clear up the institutional dimension because it's far greater than any of us can clear up ourselves. What I would recommend is be looking for those priests and bishops who will have the voice of the impassioned and energized laity. Benedict told us to take co-responsibility for the church, not merely to collaborate, not merely to cooperate, but to take co-responsibility for the church. And that means telling the truth and insisting that they tell the truth. So you're not going to have all the answers you want, you know?  So, yes. As I think your show illustrates, your daily show illustrates a lot of the answers to the cultural questions that we experience, whether we're faced with, the church's response to those requires a lot of nuance and a lot of depth of understanding. How do we reconcile that with a media that only wants sound bites? They want 30 seconds where you can't even begin to even quantify their understanding of an issue to give an explanation that makes any sense or that it's of any value. How do we respond to this? How do we deal with that? Well, it's a problem with the nature of the news. The news is, by its definition and by its own self-understanding, is interested in what's ephemeral, temporary. I mean, take a look at what we've seen with the way that Trump administration is being covered by CNN. It's a chronic story. They're treating it like a disaster story as though something went terribly wrong at the White House and they've got to be there as though, you know, the Malaysian flight disappeared and we've got to be there. And if you take a look at the discussions, the discussions never go very deep on any topic. That is the nature of news coverage. And I think that's what we say. We say that the news is about the ephemeral. It's about the temporary. It, you know, what did they use to say with newspapers? You know, one day you read them, the next day you use them to wrap fish in. That's the nature of news media. And we're not going to change that. What you can do is find programs that give you more nuance, support them, view them. There are some secular programs that are out there that are better than others. But if you're looking at like nightly news, it's hopeful. Honestly, it's hopeless. Hi, Elle. I just want to say I thank God for Archbishop Vigano and his courage. Yeah. And I love the line in his letter where he said, I'm an old man. And I'm going to be facing my judge soon. To me, that went right to the heart of it. And I wish more bishops would do that. Yeah. You know, as a lay person, I'm never going to leave the Catholic Church. I pray to God I won't. And I also know that we really don't have any power over the bishops. I'll tell you though, I love our priests. I think most of the bad ones have been sent away or have died. But I think the bishops need a lot of work. I think there's been a lot of covering up. I think some of the ones, many of the ones who are still in power have taken part in it. If only some of them would start to break this mesh work where they're all holding each other up. If they don't, I really think criminal and civil authorities are going to start to take it apart. It's going to happen. I really believe it will happen.  And I just want to say in my own family, we had a personal tragedy of a cousin of mine a year older than me who committed suicide a long time ago. And it came out years later that it was because of priestly abuse. And life ruined. He came from a wonderful family and a tortured young man at the end who took his own life. So I thank you though for talking openly about it here. Thanks, Al. Okay. Up front. So you mentioned a couple of bishops, Bishop Strickland, the late Bishop Morlino, you know, is being very faithful and courageous. What are your thoughts regarding our monies being pulled from those bishops like we're in a diocese and we know our bishop is not supportive and still struggling. What are your thoughts regarding taking that money and then donating it, you know, maybe our monthly donation, our yearly, what normally goes to the diocese and appeal, going to those bishops with a beautiful letter, thanking them for their courage and putting our money where our mouth is. Yeah. This is actually what the bishops fear. What they fear is that this is why they move like a herd. They're afraid of particular bishops becoming polarizing figures. So this is why they don't want to get involved in other people's jurisdiction. So I'm not sure that even if that were done, that the bishops who were receiving it would want anybody to know about it. And I would like to think of a way that that could happen. I'm not sure there's any way right now of doing that effectively. I guess, well, this is what I'm waiting. I'm waiting for some of these bishops to actually break ranks. And at that point, I would say yes. But until they break ranks, I'm not sure that would help very much. You might be satisfied.  And that's fine. You're responsible to the Lord for how you give. But I don't think it would work until some of these bishops decided that they were willing to be a lightning rod for these complaints. And they would do, I'll tell you, I've written to announce a bishop that I think is an outstanding bishop. And I explained to him the kind of things we're talking about today. I said, you know, you need to see what I'm seeing here. You need to understand the discontent of engaged laity. I talked to him shortly after the McCarrick, Vigano, Pennsylvania grand jury thing. And I said, this is much worse, I told him, much worse than 2002. In 2002, the engaged laity saw the bishops go to Dallas, take action. And they said, well, look, look what the bishops did. Okay. Well, yeah, it wasn't everything I want to see. But let's see if we can stabilize this ship again. We really have a zero tolerance policy. We still don't have a narrative from them, how we got to this mess. And that's what we need. We need somebody to tell us how this all happened. And when I told him that what's happening now, that was 2018, is much more severe than 2002. He said, no, that can't be. McCarrick is just one person. I said, it's not McCarrick. It's the revelation that McCarrick, who was largely responsible for portions of that 2002 agreement, he, in 2005, 2006, paid off to former seminarians with diocesan money. And in other words, he was down there and acting as though he was above board when in fact he was hiding these secrets. And we have reason to believe that there were some other bishops who believed that already. The stories about McCarrick are legion. I said, right now, the laity aren't asking, what are the bishops going to do? The engaged laity are saying, what the heck are we going to do? We have co-responsibility for this. It does make a difference. And we don't have any canonical authority as laity to do this. We have human moral authority or spiritual authority of our baptism. We've got to somehow find clergy who can help force this issue of disclosure. I'm not sure that this bishop that I wrote to telling him that this is worse than 2002 believes me to this day. But the reaction to the McCarrick incident is far more severe than what I saw in 2002. So if anybody finds bishops that want to break ranks, let me know. Way back. We got just a few more minutes. Okay, we're going to switch gears a little bit. Let's go to the abortion issue. Okay. Everybody realizes in New York they passed the bill where you can kill babies up to nine months. In your view, and I think everybody's view here, is this going to lead more to, say, people in nursing homes who are subject to the state and everything else who are a burden to the state where they could be euthanized and also to the mentally handicapped, are we leading to that direction? Give me that last, sharpen that question at the end there. Are we moving? Are we moving in that direction? Not necessarily under an administration we have now, but if we switch to a different administration, are we leading to that point where we can kill the babies up to nine months? But can we also lead to euthanizing people in nursing homes who become a burden and the handicapped where the state has to pay for them? Okay, they're no longer useful to us, so we'll just euthanize these people. Daniel Ezekiel, Dr. Ezekiel Emanuel, who was a key advisor to the construction of Obama's Affordable Care Act, wrote in the Atlantic Monthly about physician-assisted suicide and euthanasia practices in the Netherlands, which was the first country to begin doing this. And he wrote that the Netherlands, a lot of studies have been done in the Netherlands. The Netherlands studies fail to demonstrate that permitting physician-assisted suicide in euthanasia will not lead to the non-voluntary euthanasia of children that demented the mentally ill, the old, and others. Indeed, the persistence of abuse and the violation of safeguards, despite publicity and condemnation, suggests that the feared consequences of legalization are exactly its inherent consequences. In other words, watching Belgium, watching the Netherlands, what we're seeing is increasingly there are moves towards involuntary and unrequested euthanasia. We had the case of Brittany Maynard, she was 29 years old. She ended up killing herself, and CNN made her one of the 11 extraordinary people of 2014 simply for choosing her death. Once assisted suicide is praised as a laudable option, I know that there are going to be many older people who have sacrificed their lives for their children, who have lived for others, and if they begin to feel that they're a, quote, burden, and society has said, this is a way that you can relieve your loved ones of the burden that you've become. Absolutely, we're going to see older men and women make that choice, eventually. I don't have any, I look at my own mother, and I could imagine her doing that very thing. She's now 88, thankfully she's well cared for. But my point is that we're living at a time where the value of life is being reinterpreted, and we need to be the people that are on the side of the angels here. The pro-life movement has become probably the best organized political movement in America right now, and it's really anchored, and it's not time to give up. I should mention another one, too. Professor Theodor Boer, who argued in favor of a good euthanasia law in the Netherlands, said, with 12 years of experience, I now take a very different view. Cases have been reported in which a large part of the suffering of those given euthanasia or assisted suicide consisted in being aged, lonely, or bereaved. Some of these patients could have lived for years or decades. Pressure on doctors to conform to patients, or in some cases relatives wishes, can be intense. Pressure from relatives in combination with a patient's concern for their well-being is in some cases an important factor behind a euthanasia request. So I think this is where we can shine. And again, make sure that we are talking about human flourishing. We want to do what's best. I'll tell you a story just to close us off here. Who remembers Dr. Jack Kevorkian? Oh, good, good. I was hoping you'd remember him. Jack Kevorkian lived in Royal Oak, Michigan, not very far from where I used to do a program on a 50,000 watt FM station for Detroit, St. Louis, and Portland. When Kevorkian began killing people with his suicide machine, I invited him to come on the air to talk with me about it. Obviously, we were not going to agree.  And I was resisting, of course, going along with his logic. And he said, have you ever seen somebody die of Alzheimer's? I said, well, no. Actually, Dr. Kevorkian, I have not seen anybody die of Alzheimer's. You have. Tell us what you're seeing.  They are a zero on nothing. I mean, it was really fierce. I said, and I said, well, I don't think people at any point in their life are zeros or nothings. And he raved more. In the providence of God, my very next guest that day, this was unplanned, was a guy named Woodrow Worsig. He was a former editor with Newsweek. And he had written a book about his wife's trials with Alzheimer's. The book was called I Love You Too. And so he began to tell me the story about the love affair that he and his wife had right until she was quite in the last stages of Alzheimer's. And I said to him, Woody, I don't want to trespass on the sacred moments with your wife. But I just talked to this guy, Jack Kovorkian, who tells me that when people reach that stage in Alzheimer's, that they are a cipher, a zero, a nothing. They're nothing more than a mound of their own excrement. Is that what you saw with your wife? And he didn't take any offense at all. He said, no, no. He said, right up to the end, I'd... She would recognize the shuffling of my feet. I would enter the room and I would whisper, I love you. And she said, I love you too. Those are two different futures for the way we treat patients, end time Alzheimer's patients. I'm no doctor, but one thing I know, and that is if anything is worth protecting, because of its intrinsic worth and dignity, it's human beings who are made in the image and likeness of God, people for whom Christ died. And if we have to go out fighting on any front, it seems to me this, what the Catholic Church teaches, on the sanctity of human life from conception to natural death, that is worth fighting for to the end. We are the community because of the incarnation, because of the gospel, because of the teachings of St. Augustine, St. Thomas Aquinas, because of the great work of people like Cicely Saunders and the hospice movement, and because of so many people who have sacrificed to protect the unborn children. We still can claim that the Catholic Church introduced into the consciousness of the human race this idea of the sanctity of human life. That's checkmate. Everybody will have to eventually acknowledge that or go to a different type of understanding of the human person, and we won't like the alternative. So I think what you bring up is frightening. I don't think we see it in the Netherlands and see it in Belgium. Thanks very much. I think we've just gone over a few minutes here. I wish we had more time. There's so much stuff, but amen. Thank you.


I purchased the car in 1978, it was a one lady owner vehicle brought it from a friend of mine in London who was in charge of looking after the Mark II that was in Morse programme. In 1986 I decided to have a bare metal re-spray and change the colour from blue to calm and red. That was fine and I drove the car from then until 2005 when it suffered an engine fire due to the overflow issuing petrol onto the hot surface of the engine. I think when I started it up there was a spark and it ignited. This caused a singed area to the bonnet and I was advised rather than just spray the bonnet that the front of the car should be sprayed. This would match the paint on the rear which it did. Following on from that re-spray in 2005 it was noticeable in ten years later that the rear paint work had faded and turned a sort of opaque finish. So a few weeks ago there was an email from the chairman of the local Jaguar club in Derbyshire asking me if there was anyone with a car that suffered fading paint due to ultraviolet light. That's the story, that's why I'm here.


We are in Summit County at the Girls on the Run 5K event.  So Girls on the Run is really an incredible organization that is about empowering young women and through sort of learning how to run longer distances with the goal of being to run the 5K at the end, you know what we find is that these young women really gain some self-confidence and strength and learn teamwork and make new friends and try things that they never would have tried before. Not only did the girls run but they brought their families and their siblings and their friends and so it really kind of brings the whole community together. So the Summit Clinic has been terrific about supporting big community events and particularly events that encourage people to get outside and be active and use their bodies and use their minds and so the Summit Clinic and the Stem and Pillow County Research Institute are very instrumental in supporting programs like this and making sure that they happen.


Now, based on this, we can take up some problems on the equation of a norm. Let's try with this question. Prove that the line Lx plus My minus n equal to 0 will be normal to, will be normal to the standard form of the hyperbola which is x square by a square minus y square by b square equal to 1 if, if a square by L square minus a square by L square minus b square by m square is equal to a square plus b square whole square by n square. So, I would request those of you who are sitting with a pen and paper, please start working this out along with me. So, again, I will first start with the equation of the normal in the parametric form. So, we know that if I am drawing the equation of a normal at any general point, a seek phi comma b tan phi that would look like ax cos phi plus by cot phi is equal to a square plus b square. Which means I can write this equation to be this. Now, again, it's a, it's a matter of comparison. So, what I'm going to do, I'm going to compare this with Lx plus My minus n equal to 0. So, it's all about comparing these two equations because they both are representing the same equation. So, let us compare. So, when we compare, we get a cos phi by L that is the coefficient of x from in both the equations should be equal to b cot phi by m should be equal to a square plus b square by n, a square plus b square by m. Now, from this equation, I can always get my seek phi and tan phi. So, seek phi from here would be nothing but n a by l a square plus b square. And similarly, so I compare these two and I got this equation. Now, I'm comparing these two and I would get this equation that is tan of phi is b n by m a square plus b square. Now, we can use the famous trigonometric identity seek in n square phi minus tan square phi equal to 1 which will give you n square by a square by l square a square plus b square whole square minus b square by n square m square a square plus b square whole square is equal to 1 is equal to 1. So, I can always divide by n square by a square plus b square whole square. So, it will give you a square by l square minus b square by m square is equal to a square plus b square by n square. So, this is the desired condition and hence proved. Now, moving on to the next concept which is the concept of pair of tangents pair of tangents of a hyperbola. Now, guys, these concepts are all repetitive. We have already done similar concepts in parabola ellipse circle as well. So, I'm not going to repeat this same concept over and over again. So, just to quickly recall the equation of a pair of tangents to a hyperbola. Let's say I write down the equation of a hyperbola to be our general case of a hyperbola like this. Then we know that the equation of the pair of tangents would be t square is equal to s s 1 t square is equal to s s 1. So, just replacing our t with what we have learned this is the expression for t square is equal to s this is your s and this is your s 1 and this is your s 1. So, t square is equal to s s 1 becomes the equation of the pair of tangents. Similarly, chord of contact chord of contact. So, chord of contact is a chord connecting the points of contact of the tangents drawn from an external point on to the hyperbola. So, just quickly sketching the chord of contact over here. So, let's say these are your arms of the hyperbola and you have drawn two tangents. You have drawn two tangents from a point x 1 y 1. Then this line connecting let's say I call this as Q and R. Q and R will be called your chord of contact. It would be called your chord of contact and chord of contact equation is known to us as t equal to 0. A similar concept linked to this is the equation of the chord bisected at a given point equation of a chord of a chord bisected at a given point. So, if you know the midpoint of any chord let's say x 1 y 1 then the equation of the chord is given by t equal to s 1, t is equal to s 1. Where the general meaning of t s s 1 remains the same as what we had discussed earlier. So, we will quickly take a question on the concepts which we have discussed in this particular slide. So, let's begin with a question. Prove that the locus of the midpoints, the locus of the midpoints of the chords of the hyperbola x square by a square minus y square by b square equal to 1 with subtend 90 degrees at the origin with subtend 90 degree at the origin is x square by a square minus y square by b square whole square times 1 minus a square minus 1 minus 1 by b square is equal to x square a to the power 4 plus y square b to the power 4. Now the moment it comes to a line a pair of lines subtending a certain angle at the origin we actually think of the concept of homogenization. So, the hint for this problem is we can solve this problem simply by using the concept of homogenization. I have already discussed this with you in the past but while solving this problem I will discuss with you again. So, what do you have to do is in this case we have to homogenize the equation of the line which is the chord whose midpoint is let's say h comma k. So, let's say the midpoint is h comma k. So, we know t equal to s 1, t is equal to s 1. So, this is your t equal to s 1. This is the equation of a chord whose midpoint is h comma k. So, what do you have to do is we have to homogenize these two equations. Homogenize means we have to convert this together as a second degree equation which actually is representative of a pair of straight lines which passes through origin. So, how do we do that? How do we homogenize these two equations? It's very simple process. So, what do we do is we don't disturb the second degree term because they are already into second degree. Instead of this one we actually will write one square. Instead of this one we will actually write a one square and I will show you from where we will replace this one square. So, from here we can see that we can write 1 to be hx by a square minus ky by b square divided by this. So, what I will do is let me call this as 1. Let me call this as 2. We will use the second equation in the first equation. We will use the second equation in the first equation and when we do that we end up getting x square by a square minus y square by b square is equal to hx by a square minus ky by b square whole divided by h square by a square minus k square by b square the square of this entire thing. The square of this entire thing. Now, just simplifying this guys we can write it as h square by a square minus k square by b square whole square times x square by a square minus y square by b square is equal to hx by a square minus ky by b square whole square. Right? Now, what have we learned? We have learned that in any second degree equation we know that in any second degree equation which actually represents a pair of straight lines. Okay? If the lines are perpendicular to each other then a plus b is equal to 0. So, this implies the lines are perpendicular to each other. Okay? So, basically it's passing through the origin also and perpendicular to each other which is precisely what I want to address in this problem as well. Okay? So, a plus b equal to 0 means coefficients of this is coefficient of x square and this is coefficient of y square. So, coefficient of x square and coefficient of y square should add up to give you 0. So, what is the coefficient of x square? Coefficient of x square, first of all I can get x square from this expression which is actually this term and from this expression will get minus h square by a to the power 4 plus coefficient of y square again I can get it from here. Okay? And from here which is minus of k square by b to the power 4 is equal to 0. Now, I can just simply take h square by a square minus k square by b square whole square common and in the brackets I will get 1 by a square minus 1 by b square and I will take h square by a to the power 4 plus k square by b to the power 4 on the other side. So, we can now generalize this. We can now generalize this x square by a square minus y square by b square whole square 1 by a square minus 1 by b square equal to x square by a to the power 4 plus y square by b to the power 4 which actually gives you the equation of the desired locus. Okay? So, guys again I am repeating this concept. The concept of locus is of lot of importance in J. So, please practice lot of questions on locus because all the concepts which we are discussing in coordinate geometry are somehow linked to the concept of locus. Okay? So, moving on to the concept of pole and polar. Pole and polar. So, what is the concept of pole and polar? Again, very similar to what we discussed in case of circles ellipse and parabola. So, when a point is external or internal or on the hyperbola and you draw all sort of lines passing through that point. Okay? So, let us say I take one of the branches of a hyperbola and there is a point like this and let us say I draw a line through it. So, the ends of these lines let me draw tangents. Let me draw tangents. Okay? Let us say I draw another line like this. So, let me draw tangents from this point as well. Now, all these tangents, the meeting point of these tangents will lie on a straight line and that straight line is called the polar for this pole. The straight line is called the polar for this point which is called the pole. Okay? So, not a new concept. I have already discussed with you and I have also discussed with you that when the point is on the hyperbola, the polar is basically nothing but the tangent drawn at that point. Right? And when it is outside the hyperbola, it is going to be the chord of contact. So, in all the cases, the equation of the, the equation of the polar is going to be t equal to 0. The equation of the polar is going to be t equal to 0. Now, based on this, I would like to just take up a simple problem. Again, a locus-based problem. Find the locus of, find the locus of the poles of normal chords of the hyperbola, x square by a square minus y square by b square equal to 1. So, find the locus of the poles of normal chords. So, what is the meaning of a normal chord? So, chord which is also normal to the hyperbola. So, we have to find what is the locus of the poles of all normal chords to this hyperbola. Again, it is a simple concept which is based on the understanding of locus. So, let us start with the equation. So, let us say the pole b h comma k. The pole b h comma k. So, we know that the equation of the polar, equation of the polar would be t equal to 0. That is h x by a square minus y k by b square equal to 1. And let us say this is also behaving as a normal. Let us say this polar is also a normal at the point, at the point a seek phi comma b tan phi. So, the equation of the normal would be nothing but a x cos phi plus b y cot phi is equal to a square plus b square. Now, these two equations 1 and 2 they are same. So, comparing equation 1 and 2 since they represent the same thing, I can write h by a square divided by a cos phi is equal to minus y by b sorry minus k by b square divided by b cot phi is equal to 1 by a square plus b square. So, from here we can get seek phi as a cube by h times 1 by a square plus b square. So, by comparing these two I can always get my seek phi like this and a similar way by comparing these two I can get tan phi as minus b cube by k 1 by a square plus b square. Now, the next step is very simple. We have to eliminate our phi. That means we have to make use of trigonometric identity which is nothing but seek phi minus tan phi seek square phi minus tan square phi is equal to 1 which ends up giving us a to the past 6 by h square times 1 by a square plus b square whole square minus b to the power 6 by k square a square plus b square whole square equal to 1. Now, we can further simplify this as a to the power 6 by h square minus b to the power 6 by k square is equal to a square plus b square whole square. And now we can generalize this as a to the power 6 by x square minus b to the power 6 by y square equal to a square plus b square whole square. So, this is the required locus for the poles of the normal quads of the hyperbola. Now, moving on to the next concept which is the concept of diameter, which is the concept of diameter of a hyperbola. So, first of all, let us define the diameter. So, the diameter is nothing but the locus of the middle points or midpoints of a system of parallel quads of a system of parallel quads, okay. This is called the diameter of the any conic section. In fact, in circle also the same definition will be true, in parabola also the same definition will be true, in ellipse also the same definition would be true. So, now let us move to the equation of the diameter. We can prove the equation of a diameter as y is equal to b square x by a square m, okay, where m is the slope of the system of quads, slope of the parallel quads, which is bisected by the diameter, slope of the parallel quads, okay, of the parabola, sorry of the hyperbola x square by a square minus y square by b square equal to 1, okay. So, how do we prove this? Again, the proof is very simple, it comes from the concept of the equation of a chord whose midpoint is known. So, what we will do is, since the diameter is the locus of the midpoint of the parallel quads, I will say let the midpoint of the parallel chord be let the midpoint of the parallel quads be h comma k. So, h comma k is a variable point, okay. So, t equal to s 1 would be the equation of the chord whose midpoint is h comma k. So, t equal to h 1 will be t equal to s 1 will be this. Now, I am only claiming that this equation has a slope of m because all these quads are having a slope of m, right. So, what I am going to do is, I am going to write down the slope which is in this case will be h b square by a square k to be equal to m and that is it. We have to just generalize our k with y and h with x. So, it becomes b square x by a square y equal to m which means y is equal to b square x by a square m is the desired equation of the diameter having a slope diameter bisecting all the quads having a slope of m.


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