Coordinate Geometry: JEE Main 2026 Mathematics question

Let a focus of the ellipse $E: \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ be $S(4, 0)$ and its eccentricity be $\frac{4}{5}$. If the point $P(3, \alpha)$ lies on E and O is the origin, then the area of $\Delta POS$ is equal to: