Let H_1: \frac{x^2}{a^2}-\frac{y^2}{b^2}=1 and H_2:-\frac{x^2}{A^2}+\frac{y^2}{B^2}=1 be two hyperbolas having length of latus rectums 15 \sqrt{2} and 12 \sqrt{5} respectively. Let their eccentricities 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 e_2^2 is equal to . [24 Jan 2025 Shift 2]

Hyperbola

Section: Mathematics

Question : 16 of 92

Marks: +1, -0

Let H1:‌

−‌

=1 and H2:−‌

+‌

=1 be two hyperbolas having length of latus rectums 15√2 and 12√5 respectively. Let their eccentricities be e1=√‌

and e2 respectively. If the product of the lengths of their transverse axes is 100√10, then 25e22 is equal to ‌‌‌‌ .

[24 Jan 2025 Shift 2]

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