JEE Advanced 2016 Paper 1 Mathematics Q12

Mathematics

Problem

The circle C1:x2+y2=3C_1:x^2+y^2=3, with centre at OO, intersects the parabola x2=2yx^2=2y at the point PP in the first quadrant. Let the tangent to the circle C1C_1 at PP touches other two circles C2C_2 and C3C_3 at R2R_2 and R3R_3, respectively. Suppose C2C_2 and C3C_3 have equal radii 232\sqrt3 and centres Q2Q_2 and Q3Q_3, respectively. If Q2Q_2 and Q3Q_3 lie on the yy-axis, then

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