# How to compute the cross point between an ellipse and a straight line?

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.

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''.