Let the eccentricity of the hyperbola H : x^ 2 /a^ 2 - y^ 2 /b^ 2 = 1 be 5/2 and length of its latus rectum be 6 2 . If y = 2x + c is a tangent to the hyperbola H, then the value of c^ 2 is equal to

JEE Main 2022 Mathematics question

Let the eccentricity of the hyperbola H : be and length of its latus rectum be . If y = 2x + c is a tangent to the hyperbola H, then the value of is equal to

(1)18
(2)20Correct
(3)24
(4)32

Answer: (2)

Solution

, so . The length of the latus rectum is , so (3/2)a =

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Question ID VK-034968