Answer
$x^2=-100y$
Work Step by Step
Standard form of a parabola is given as: $x^2=4py$ ...(1)
Formula to find focus is: $F(0,p)$ and formula to find directrix is: $y=-p$
As we are given that focus is: $(0,-25)$ and directrix is: $y=25$
Plug all these data in equation (1), we have: $p=-25$
Thus, $x^2=4(-25)y \implies x^2=-100y$
