# Thread: Intersection of an ellipse and a parabola

1. ## Intersection of an ellipse and a parabola

The ellipse and parabola are in their canonical forms, that is the
elipse is x^2/a^2 + y^2/b^2 = 1

and the parabola is y^2 = 2px

The qustion says find coordinates of the points where the parabola and the ellipse intersect in terms of the semiaxes of the ellipse and the focal parameter of the parabola. I take that to mean find the coordinates of intersection in terms of a,b, and p, but how?

I tried making both equations first equal to zero, then equal to each other, but hit a dead end.

Suggestions?

2. That just gives you a single equation in both unknowns, which kind of defeats the purpose! Whatever method you use, your goal is to get an equation in a single unknown. Your second equation says that $y^2= 2px$. Replace the " $y^2$" in the ellipse equation to get a single quadratic equation in x.