Let S be the focus of the hyperbola x^2/3-y^2/5=1, on the positive x -axis. Let C be the circle with its centre at A (√ 6, √ 5 ) and passing through…

Let $\displaystyle S$ be the focus of the hyperbola $\displaystyle \frac{x^2}{3}-\frac{y^2}{5}=1$, on the positive $\displaystyle x$-axis. Let $\displaystyle C$ be the circle with its centre at $\displaystyle \mathrm{A}(\sqrt{6}, \sqrt{5})$ and passing through the point S . If O is the origin and SAB is a diameter of C , then the square of the area of the triangle OSB is equal to $\displaystyle \_\_\_\_$