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Hyperbola question

2025 · 7 Apr · Shift 1 · Q50

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JEE Main
Mathematics
Hyperbola
2025 · 7 Apr · Shift 1 · Q50

Hyperbola question

2025 · 7 Apr · Shift 1 · Q50

JEE MainMathematicsHyperbolaNumerical+4 / −1

Consider the hyperbola

\frac{x^2}{a^2}-\frac{y^2}{b^2}=1

having one of its focus at

\mathrm{P}(-3,0)

. If the latus ractum through its other focus subtends a right angle at P and

a^2 b^2=\alpha \sqrt{2}-\beta, \alpha, \beta \in \mathbb{N}

, then

\alpha+\beta

is

\underline{\hspace{2cm}}

.

Numerical answer

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