JEE Main202621 January 2026Morning ShiftMathematicsHyperbolaActual

Let the foci of a hyperbola coincide with the foci of the ellipse x² 36 + y² 16 =1 . If the eccentricity of the hyperbola is 5, then the length of its latus rectum is :

Options

A16
B24 5
C12
D96 5

Correct 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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