# What is the vertex form of the equation of the parabola with a focus at (6,-13) and a directrix of y=13 ?

Sep 12, 2017

$y = \setminus \frac{1}{- 52} {\left(x - 6\right)}^{2} + 0$

#### Explanation:

Given the focus and directrix of a parabola, you can find the parabola's equation with the formula:

$y = \setminus \frac{1}{2 \left(b - k\right)} {\left(x - a\right)}^{2} + \setminus \frac{1}{2} \left(b + k\right)$,

where:

$k$ is the directrix &

$\left(a , b\right)$ is the focus

Plugging in the values of those variables gives us:

$y = \setminus \frac{1}{2 \left(- 13 - 13\right)} {\left(x - 6\right)}^{2} + \setminus \frac{1}{2} \left(- 13 + 13\right)$

Simplifying gives us:

$y = \setminus \frac{1}{- 52} {\left(x - 6\right)}^{2} + 0$