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Please let me know how to compute the possible cross points between an ellipse and a straight line. In details , I know the basic properties of the two shapes. So if the ellipse had its center at the origin and its axes were same as the XY axes then I could compute the cross points.

Thank you in advance.

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up vote 3 down vote accepted

Just solve the system of equations $$ \eqalign{&{x^2\over a^2}+{y^2\over b^2}=1\cr &y=mx+c} $$ using the substitution method.

I assume by ''cross point'' you mean ``intersection point''.

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