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JEE Main 2022 Mathematics question

MathematicsEllipseJEE Main 2022

Let the common tangents to the curves and intersect at the point Q. Let an ellipse, centered at the origin O, has lengths of semi-minor and semi-major axes equal to OQ and 6, respectively. If e and respectively denote the eccentricity and the length of the latus rectum of this ellipse, then is equal to .

Answer: 4

Solution

A tangent to is y = mx + 1/m. It touches (radius 3/2) when 1/|m| = , so = (9/4)(1 + ), which gives . The common tangents are $y = ±

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Question ID VK-025366