An ellipse and a hyperbola have the same foci, $A$ and $B$, and intersect at four points. The ellipse has major axis 50, and minor axis 40. The hyperbola has conjugate axis of length 20. Let $P$ be a point on both the hyperbola and ellipse. What is $PA \cdot PB$?

Answer 1

Stop Cheating! Thankfully, the answer isn't 600.

Answer 2

500