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JEE Advanced 2016 Paper 1 Mathematics Question 48

The circle \(C_1 : x^2 + y^2 = 3\), with centre at O, intersects the parabola \(x^2 = 2y\)  at the pont P in the first quadrant. Let the tangent to the circle \(C_1\) at P touches other two circles \(C_2\) and \(C_3\) at \(R_2\) and \(R_3\), respecticely. Suppose \(C_2\) and \(C_3\) have equal radii \(2 \sqrt{3}\) and centres \(Q_2\) and \(Q_3\), respectively. If \(Q_2\) and \(Q_3\) lie on the \(y\)-axis, then

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