Let m_1 and m_2 be the slopes of the tangents drawn from the point P (4,1) to the hyperbola H: y^2/25-x^2/16=1. If Q is the point from which the…

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