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JEE Main 2015 Mathematics question

MathematicsParabolaJEE Main 2015

If the tangent to the conic, at touches the circle, (for some fixed ) at a point ; then is

Answer: (2)

Solution

Differentiating gives at , so the tangent is , i.e. . The circle has centre . Since the line touches the circle, the point of contact is the foot of the perpendicular from to the line. Using the

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Question ID VK-115295