The circle `C_(1) : x^(2)+y^(2)=3`, with cenre at O, intersects the parabola `x^(2)=2y`

The circle `C_(1) : x^(2)+y^(2)=3`, with cenre 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 `2sqrt(3)` and centres `Q_(2)` and `Q_(3)` respectively. If `Q_(2)` and `Q_(3)` lie on the y-axis, then `Q_(2)Q_(3)=`