JEE Advanced 2015 Mathematics question
Consider the hyperbola and a circle with center . Suppose that and touch each other at a point with and . The common tangent to and at intersects the -axis at point . If is the centroid of the triangle , then the correct expression(s) is(are)
Answer: (A),(B),(D)
Solution
Tangent to at : , meeting the -axis at . The circle touches at , so its centre lies on the normal at : ; with , , so . Centroid:
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