For some (0, 2 ), let the eccentricity and the length of the latus rectum of the hyperbola x^ 2 -y^ 2 ^ 2 =8 be e_ 1 and l_ 1 , respectively, and let the eccentricity and the length of the latus rectum of the ellipse x^ 2 ^ 2 +y^ 2 =6 be e_ 2 and l_ 2 , respectively. If e_ 1 ^ 2 =e_ 2 ^ 2 ( ^ 2 +1 )

Question

For some (0, 2 ), let the eccentricity and the length of the latus rectum of the hyperbola x^ 2 -y^ 2 ^ 2 =8 be e_ 1 and l_ 1 , respectively, and let the eccentricity and the length of the latus rectum of the ellipse x^ 2 ^ 2 +y^ 2 =6 be e_ 2 and l_ 2 , respectively. If e_ 1 ^ 2 =e_ 2 ^ 2 ( ^ 2 +1 ), then ( l_ 1 l_ 2 e_ 1 e_ 2 ) ^ 2 is equal to \_\_\_\_

Quantrex Academy · Accepted Answer

Correct answer: A. A

x^2 8 - y^2 8 ^2 = 1, e_1 = 1 + 8 ^2 8 _1 = 2b^2 a = 2 (8 ^2 ) 2 2 x^2 6 + y^2 6 ^2 = 1; e_2 = 1 - 6 ^2 6 = _2 = 2b^2 a = 2 6 ^2 6 e_1^2 = e_2^2(1 + ^2 ) 1 + ^2 = ^2 (1 + 1 ^2 ) 1 + ^2 = ^2 + ^2 Solving we get = 4 _1 = 2 2 e_1 = 3 2 _2 = 6 e_2 = 1 2 ( _1 _2 e_1 e_2 ) ^2 = 8 (By putting values)

JEE Main Mathematics Question (2026) — Solution

Question

Options

Answer

Step-by-step solution