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Analyzing the coefficients of the quadratic equation

  1. Jul 31, 2015 #1
    Is possible classify the quadric equation Axx + Bxy + Cyx + Dyy + Ex + Fy + G = 0 how straight, hyperbola, circle, ellipse, parabola, etc, in the same way that is did in the phase plan:

    https://upload.wikimedia.org/wikipedia/commons/3/35/Phase_plane_nodes.svg

    https://upload.wikimedia.org/wikipedia/commons/3/35/Phase_plane_nodes.svg

    I tried this, but, for some reason, don't works... Can you help me!?
     
  2. jcsd
  3. Jul 31, 2015 #2
  4. Aug 1, 2015 #3
    I want to express the quadric equation in this way: [tex]
    \begin{bmatrix}
    A & B \\
    C & D
    \end{bmatrix}
    :
    \begin{bmatrix}
    x^2 & xy \\
    yx & y^2
    \end{bmatrix}
    +
    \begin{bmatrix}
    E\\
    F
    \end{bmatrix}
    \cdot
    \begin{bmatrix}
    x\\
    y
    \end{bmatrix}
    +
    G=0
    [/tex]

    And I want to analyze the square matrix, the first matrix, the matrix of the coefficients.
     
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