# What is the standard form of the equation of the parabola with a directrix at x=-5 and a focus at (-6,7)?

Aug 6, 2018

${\left(y - 7\right)}^{2} = - 2 \left(x + 5.5\right)$

#### Explanation:

Given -

Focus $\left(- 6 , 7\right)$
Directrix $x = - 5$

Vertex $\left(- 5.5 , 7\right)$

$a = 0.5$

Then the formula for the parabola is -

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

${\left(y - 7\right)}^{2} = - 4 \left(0.5\right) \left(x + 5.5\right)$

${\left(y - 7\right)}^{2} = - 2 \left(x + 5.5\right)$