Let a focus of the ellipse E: x^2/a^2+y^2/b^2=1 be S (4,0) and its eccentricity be 4/5. If the point P (3, α) lies on E and O is the origin, then the…

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