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Hyperbola question

2024 · 8 Apr · Shift 2 · Q54

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JEE Main
Mathematics
Hyperbola
2024 · 8 Apr · Shift 2 · Q54

Hyperbola question

2024 · 8 Apr · Shift 2 · Q54

JEE MainMathematicsHyperbolaNumerical+4 / −1

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

\underline{\hspace{2cm}}

.

Numerical answer

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