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Intersection of Conic Sections


This seems like a simple question, but I am finding it diffucult to
find a simple solution.

What are the points of intersection of

0 = A1 + A2*x + A3*y + A4*x^2 + A5*x*y + A6*y^2

and

0 = B1 + B2*x + B3*y + B4*x^2 + B5*x*y + B6*y^2


where Ai and Bi are constants.

When I solve this with mathematica, I get a rather complex expression.
Is there a simple algorithm that finds all the roots?

Cheers,
Irchans


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