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?