The equation of an ellipse is
\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1.
Point $Q$ is at $(0,b).$ Points $P$ and $R$ lie on the ellipse so that $\overline{PR}$ is parallel to the $x$-axis, and sides $\overline{QR}$ and $\overline{PQ}$ contain foci $F_1$ and $F_2,$ respectively. If $a=8$ and $b=3$, then find the area of triangle $PQR$.
