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Conic sections

  1. Oct 20, 2007 #1
    I have a hyperbola with the following equation and I am trying to find my angles to eventually rotate this (conic section), but I don't know what to do because when I follow the standard form of (A-C)/B, I get zero. Is there some trick that I don't know about.

    x^2+4xy+y^2=12
     
  2. jcsd
  3. Oct 21, 2007 #2
    First, you can write the equation in this way
    [tex]
    \left[ \begin{array}{cc}
    x & y
    \end{array} \right]
    \cdot
    \left[ \begin{array}{cc}
    1 & 2 \\
    2 & 1
    \end{array} \right]
    \cdot
    \left[ \begin{array}{c}
    x \\ y
    \end{array} \right] = 12
    [/tex]

    Now, you have to diagonalize the symmetric matrix
    [tex]
    A = \left[ \begin{array}{cc}
    1 & 2 \\
    2 & 1
    \end{array} \right]
    [/tex]

    Then, see this!
     
  4. Oct 21, 2007 #3
    I have never seen this technique before is that the only way to do this?
     
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