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JEE Main 2016 Mathematics question

MathematicsHyperbolaJEE Main 2016

Let and respectively be the semi-transverse and semi-conjugate axes of a standard hyperbola whose eccentricity satisfies the equation . If is a focus and is the corresponding directrix of this hyperbola, then is equal to

Answer: (1)

Solution

Solve for the eccentricity: factorises as , giving or . A hyperbola requires , so . The focus is at , so \frac$53

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Question ID VK-115566