Coordinate Geometry: JEE Main 2023 Mathematics question

Let $m_{1}$ and $m_{2}$ be the slopes of the tangents drawn from the point $\mathrm{P}(4,1)$ to the hyperbola $H: \frac{y^{2}}{25}-\frac{x^{2}}{16}=1$. If $\mathrm{Q}$ is the point from which the tangents drawn to $\mathrm{H}$ have slopes $\left|m_{1}\right|$ and $\left|m_{2}\right|$ and they make positive intercepts $\alpha$ and $\beta$ on the $x$-axis, then $\frac{(P Q)^{2}}{\alpha \beta}$ is equal to __________.