Lines $L_1$ & $L_2$ are rotating in an anticlockwise direction about the points $A\left(–2,0\right)$ and $B\left(2,0\right)$ respectively in such a way that the speed of angle of rotation of line $L_2$ is double as that of $L_1.$ Initially equations of both lines are $y=0.$ If the angle of rotation of line $L_2$ varies between $0$ to $\frac{\pi }{2}$, then the locus of the point of intersection $P$ of lines $L_1$ & $L_2$ is part of a circle whose radius is equal to