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I am looking for an algorithm for finding the intersection of a line and an ellipse.

I have the line in the form

$ax+by+c=0 \qquad(1)$

and the ellipse in the form

$Ax^2+Bxy+Cy^2+Dx+Ey+F=0 \qquad(2)$

My idea is to solve in a closed form the system $(1),(2)$. Is it too naive? What are the pitfalls of such approach?

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    @whuber: Good point!2011-06-07

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