A circle passing through the point $P(\alpha, \beta)$ in the first quadrant touches the two coordinate axes at the points $A$ and $B$. The point $P$ is above the line $A B$. The point $Q$ on the line segment $A B$ is the foot of perpendicular from $P$ on $A B$. If $P Q$ is equal to 11 units, then the value of $\alpha \beta$ is ___________.