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