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Help with determining Angle of Rotation for a Conic, please.

  1. Dec 9, 2007 #1
    I am looking for the angle needed to rotate the conic to eliminate the xy-term
    but the angle I find is negative and I need the counter-clockwise angle of rotation to satisfy 0 < theta < 90 degrees. Where am I going wrong? Or what else do I need to know? Thank you for your help.

    I have this equation of a conic and I am supposed to find only the angle of rotation with this formula:

    cot 2(theta) = A - C / B

    The equation I am using is this:

    153x^2 - 192 xy + 97y^2 - 30x -40y - 200 = 0​

    I then solve for theta plugging these A = 153 , B = -192 , C = 97 into
    cot 2(theta) = A - C / B

    I get this equation: cot 2(theta) = -56/192

    Let theta = 2*theta

    Then :
    cot theta = -56/192

    I take the inverse tangent to find 2*theta and then solve for theta like this:
    arctan ( 192/-56) = -73.7398 degrees

    Remember I let theta = 2*theta

    -73.7398 = 2*theta

    theta = -37 degrees.

    Is there a way for -37 degrees to satisfy the original question?
    Last edited: Dec 9, 2007
  2. jcsd
  3. Dec 10, 2007 #2


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    Staff Emeritus
    Science Advisor

    If one axis of the ellipse is at -37 degrees then the other axis, at right angles to that, is 90- 37= 53 degrees.
  4. Dec 10, 2007 #3
    i get it, thank you very much.