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 two other 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. Let $Q_2 and Q_3$ lies on the y-axis.