Let H₁: (x²)/(a²) - (y²)/(b²) = 1 and H₂: -(x²)/(A²) + (y²)/(B²) = 1 be two hyperbolas having length of latus rectums 15 √(2) and 12 √(5) respectively. Let their eccentricities be e₁ = √(5/2) and e₂ respectively. If the product of the lengths of their transverse axes is 100 √(10), then 25 e₂² is equal to:

Unclassified (maths): JEE Main 2025 Mathematics question

JEE Main 2025 · January, Unspecified (session-level dataset) · Q200

JEE Main 2025January, Unspecified (session-level dataset)MathematicsMediumUnclassified (maths)

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:

Your answerInteger or decimal