Question
Let the foci of a hyperbola coincide with the foci of the ellipse x^ 2 36 + y^ 2 16 =1. If the eccentricity of the hyperbola is 5, then the length of its latus rectum is :
JEE Main
Mathematics
Hyperbola
2026
JEE Main 2026 (21 January Shift 1)
JEE Main Mathematics Question (2026) — Solution
Options
- A. 16
- B. 24 5
- C. 12
- D. 96 5
Answer
D. 96 5
Step-by-step solution
For ellipse x^2 36 + y^2 16 = 1: a = 6, b = 4, c = 36-16 = 2 5 . Foci of ellipse: ( 2 5 , 0). For hyperbola with eccentricity e = 5 and foci at ( 2 5 , 0): e = C A A = 2 5 5 . C^2 = A^2 + B^2 20 = 4 5 + B^2 B^2 = 96 5 . Latus rectum = 2B^2 A = 2 96 5 2 5 5 = 96 5 .
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