Hyperbola

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 __________.