Let $m_1$ and $m_2$ be the slopes of the tangents drawn from the point $P(4,1)$ to the hyperbola $H: \frac{y^2}{25}-\frac{x^2}{16}=1$. If $Q$ is the point from which the tangents drawn to $H$ have slopes $|m 1|$ and $|m 2|$ and they make positive intercepts $\alpha$ and $\beta$ on the x-axis, then $\frac{(P Q)^2}{\alpha \beta}$ is equal to $\_\_\_\_$ .