Let P ((2 √ 3)/(√ 7), 6/(√ 7)), Q, R and S be four points on the ellipse 9 x^2+4 y^2=36. Let PQ and RS be mutually perpendicular and pass through the…

Let $\displaystyle \mathrm{P}\left(\frac{2 \sqrt{3}}{\sqrt{7}}, \frac{6}{\sqrt{7}}\right), \mathrm{Q}, \mathrm{R}$ and S be four points on the ellipse $\displaystyle 9 x^2+4 y^2=36$. Let PQ and RS be mutually perpendicular and pass through the origin. If $\displaystyle \frac{1}{(P Q)^2}+\frac{1}{(R S)^2}=\frac{p}{q}$, where $\displaystyle p$ and $\displaystyle q$ are coprime, then $\displaystyle p+q$ is equal to