Coordinate Geometry: JEE Main 2024 Mathematics question

Let $P$ be a point on the hyperbola $H: \frac{x^2}{9}-\frac{y^2}{4}=1$, in the first quadrant such that the area of triangle formed by $P$ and the two foci of $H$ is $2 \sqrt{13}$. Then, the square of the distance of $P$ from the origin is