Let the product of the focal distances of the point P (4,2 √ 3 ) on the hyperbola H: x^2/a^2-y^2/b^2=1 be 32. Let the length of the conjugate axis of…

Let the product of the focal distances of the point $\displaystyle \mathbf{P}(4,2 \sqrt{3})$ on the hyperbola $\displaystyle \mathrm{H}: \frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ be $\displaystyle 32$ . Let the length of the conjugate axis of H be $\displaystyle p$ and the length of its latus rectum be $\displaystyle q$. Then $\displaystyle p^2+q^2$ is equal to $\displaystyle \_\_\_\_$