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Hyperbola question

2025 · 24 Jan · Shift 2 · Q50

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JEE Main
Mathematics
Hyperbola
2025 · 24 Jan · Shift 2 · Q50

Hyperbola question

2025 · 24 Jan · Shift 2 · Q50

JEE MainMathematicsHyperbolaNumerical+4 / −1

Let

\mathrm{H}_1: \frac{x^2}{\mathrm{a}^2}-\frac{y^2}{\mathrm{~b}^2}=1

and

\mathrm{H}_2:-\frac{x^2}{\mathrm{~A}^2}+\frac{y^2}{\mathrm{~B}^2}=1

be two hyperbolas having length of latus rectums

15 \sqrt{2}

and

12 \sqrt{5}

respectively. Let their ecentricities be

e_1=\sqrt{\frac{5}{2}}

and

e_2

respectively. If the product of the lengths of their transverse axes is

100 \sqrt{10}

, then

25 \mathrm{e}_2^2

is equal to

\underline{\hspace{2cm}}

.

Numerical answer

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