Conic Sections · Superchallenge problem

The ellipse $\dfrac{x^2}{49} + \dfrac{y^2}{24} = 1$ and the hyperbola $\dfrac{x^2}{9} - \dfrac{y^2}{16} = 1$ have the same foci $F_1$ and $F_2$. Let $P$ be any one of the points where the two curves meet. Find $PF_1\cdot PF_2$.