What is the equation in standard form of the parabola with a focus at (13,0)...

Explanation:
With the given point (13,0) and directrix x=-5, we can calculate the p in the equation of the parabola which opens to the right. We know that it opens to the right because of the position of the focus and directrix.
${\displaystyle {(y-k)}^2=4p(x-h)}$
From -5 to +13, that is 18 units, and that means the vertex is at (4,0). With p=9 which is 1/2 the distance from focus to directrix.
The equation is
${\displaystyle {(y-0)}^2=36(x-4)}$ Vertex Form
or ${\displaystyle y^2=36(x-4)}$