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10-2. Parabola, Ellipse, Hyperbola
hard
Let $S$ be the focus of the hyperbola $\frac{x^2}{3}-\frac{y^2}{5}=1$, on the positive $\mathrm{x}$-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 ....................
A
$48$
B
$46$
C
$40$
D
$12$
(JEE MAIN-2024)
Solution

$Image$
Area $=\frac{1}{2}(\mathrm{OS}) \mathrm{h}=\frac{1}{2} \sqrt{8} 2 \sqrt{5}=\sqrt{40}$
Standard 11
Mathematics