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