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## How to solve a bivariate quadratic equation? [closed]

I have an equation: Ax² + By² + 2Cxy + 2Dx + 2Ey + F = P

A,B,C,D,E,F and P are constants.

Now I'd need to find out the solutions in range: x+y <= 1 and x >= 0, y >= 0.

How to solve it?

(I can solve a ray intersection with quadratic bezier triangle by using the solution of this equation)

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This question is probably too low level for this site. I'd suggest transforming your conic section (your "bivariate quadratic" equation) into a standard form and then writing down parametric equations for the solution (see e.g. en.wikipedia.org/wiki/Rotation_of_axes and en.wikipedia.org/wiki/Conic_section#Standard_form). Then it's not hard to find the intersection of the conic curve with the triangle you've specified. – jc Mar 21 2010 at 19:02
Completing the squares is your ally. – Ryan Budney Mar 21 2010 at 21:15