Let H_1 : x^2 a^2 - y^2 b^2 =1 and H_2 : x^2 A^2 + y^2 B^2 =1 be two hyperbolas having length of latus...

Question

Let H_1 : x^2 a^2 - y^2 b^2 =1 and H_2 : x^2 A^2 + y^2 B^2 =1 be two hyperbolas having length of latus rectums 15 2 and 12 5 respectively. Let their eccentricities be e_1= 5 2 and e_2 respectively. If the product of the lengths of their transverse axes is 100 10 , then 25e_2^2 is equal to _____

Accepted Answer

55

JEE Main 2025 Mathematics question

Solution