# What is the equation in standard form of the parabola with a focus at (13,0) and a directrix of x= -5?

${\left(y - 0\right)}^{2} = 36 \left(x - 4\right) \text{ }$Vertex Form
or ${y}^{2} = 36 \left(x - 4\right)$

#### Explanation:

With the given point $\left(13 , 0\right)$ 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.

${\left(y - k\right)}^{2} = 4 p \left(x - h\right)$

From $- 5$ to $+ 13$, that is 18 units, and that means the vertex is at $\left(4 , 0\right)$. With $p = 9$ which is 1/2 the distance from focus to directrix.

The equation is

${\left(y - 0\right)}^{2} = 36 \left(x - 4\right) \text{ }$Vertex Form
or ${y}^{2} = 36 \left(x - 4\right)$

God bless....I hope the explanation is useful.