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