Change of Variables & the Jacobian · Superchallenge problem

Let $E$ be the elliptical region $\dfrac{16x^2}{25} + \dfrac{16y^2}{9} \le 1$, whose foci are $(\pm1, 0)$, and let $r_1$ and $r_2$ denote the distances from $(x,y)$ to $(1,0)$ and to $(-1,0)$. Evaluate $\displaystyle\iint_E \dfrac{dA}{r_1 r_2}$.