The circle  $C_1:x^2+y^2=3$  with centre at $O$  intersects the parabola $x^2=2y$  at the point $P$  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  $R_3,$ respectively. 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