JEE Main 2022 Mathematics question
An ellipse E : passes through the vertices of the hyperbola H : = −1. Let the major and minor axes of the ellipse E coincide with the transverse and conjugate axes of the hyperbola H, respectively. Let the product of the eccentricities of E and H be 1/2. If is the length of the latus rectum of the ellipse E, then the value of is equal to .
Answer: 1552
Solution
The vertices of the hyperbola H : are (0, ). The ellipse passes through them, so (the major axis being along y, b > a). Then = and = + 49/64) =
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