Question

Let m1 and m2 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 |m1| and |m2| and they make positive intercepts α and β on the x-axis, then $\frac{( P Q ) ^2}{ α β}$ α β is equal to _____.

Answer 1

The correct answer is: 8