For the hyperbola H : x^ 2 - y^ 2 = 1 and the ellipse E : x^ 2 /a^ 2 + y^ 2 /b^ 2 = 1, a b 0, let the (1)...

Question

For the hyperbola H : x^ 2 - y^ 2 = 1 and the ellipse E : x^ 2 /a^ 2 + y^ 2 /b^ 2 = 1, a > b > 0, let the (1) eccentricity of E be reciprocal of the eccentricity of H, and (2) the line y = 5/2 x + K be a common tangent of E and H. Then 4(a^ 2 + b^ 2 ) is equal to _____ .

Accepted Answer

3

JEE Main 2022 Mathematics question

Solution

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