Maths Question 23 – JEE-MAIN 2026

Let A, B be points on the two half-lines $x-\sqrt{3}|y|=\alpha$, $\alpha >0$ at a distance of $\alpha$ from their point of intersection P. The line segment AB meets the angle bisector of the given half-lines at the point Q. If $PQ=\frac{9}{2}$ and R is the radius of the circumcircle of $\mathrm{△}PAB$, then $\frac{{\alpha }^2}{R}$ is equal to _______