Maths Question 22 – JEE-MAIN 2025

Let the lengths of the transverse and conjugate axes of a hyperbola in standard form be $2a$ and $2b$, respectively, and one focus and the corresponding directrix of this hyperbola be $(-5,0)$ and $5x+9=0$, respectively. If the product of the focal distances of a point $(\alpha ,2\sqrt{5})$ on the hyperbola is $p$, then $4p$ is equal to _______.