Coordinate Geometry: JEE Main 2023 Mathematics question

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