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

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