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Finding Axes of Conic Section Equation

  1. Jan 4, 2009 #1

    I've been stuck on this for a few days now.

    I am trying to determine the X and Y axis of the general conic section equation:

    Q(x,y)=Ax^2 +Bxy+Cy^2 +Dx+ Ey+F =0

    I have A, B, C, D, E, and F.

    I have already determined the center coordinates, but I have not found information on how to find the two minor and major axes of the equations.

    Any help is appreciated. Thanks

  2. jcsd
  3. Jan 5, 2009 #2


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    Welcome to PF!

    Hi aamirnshah! Welcome to PF! :smile:

    They'll be the eigenvectors of the matrix (A B/2; B/2 C).

    Alternatively, just apply the formula for rotating coordinates through a particular angle to the original equation so as to produce an xy term of zero. :wink:
  4. Jan 5, 2009 #3
    Re: Welcome to PF!

    Wow thanks for the quick reply. So I have obtained the eigenvector of the matrix (A B/2; B/2 C). From my research I have determined that I also need to determine the eigenvalues of that matrix. But from here, I am still confused. How does this relate to knowing the 'a' and the 'b' in the equation:

    x^2 / a^2 - y^2 / b^2 = 1
  5. Jan 6, 2009 #4


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    Hint: what are the eigenvalues associated with x2/a2 - y2/b2 = 1? :wink:
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