Hi, please send me how find discriminant of a elliptic curve with two variable..
urgent please send me any reference url' s
I think this is what you mean. The method is similar for classifying PDE's as well.
The general form of an ellipse is
$\displaystyle Ax^2+By^2+Cxy+Dx+Ey+F=0$
This is a quadratic form and can be written as a matrix as follows
$\displaystyle \begin{bmatrix}x & y \end{bmatrix}\begin{bmatrix}A & \frac{C}{2} \\ \frac{C}{2} & B \end{bmatrix}\begin{bmatrix}x \\ y \end{bmatrix}+\begin{bmatrix}D && E \end{bmatrix}\begin{bmatrix}x \\ y \end{bmatrix}+F=0 $
The first matrix is always real symmetric and can be diagonalized and its discriminant is the sum of its eigenvalues.
I hope this is what you were looking for!