QJEEM24Macb05: JEE Main 2024 Mathematics - Class 11 JEEM24Macb05 Solution: Let be the focus of the hyperbola , on the positive -axis. Let…

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