# How do you find the equation of the parabola with the given focus F(-2,0) and directrix x=8?

Aug 9, 2017

The equation of the parabola is ${y}^{2} = - 20 \left(x - 3\right)$

#### Explanation:

Any point $\left(x , y\right)$ on the parabola is equidistant from the focus $F = \left(- 2 , 0\right)$ and the directrix $x = 8$

Therefore,

$\sqrt{{\left(x + 2\right)}^{2} + {\left(y\right)}^{2}} = x - 8$

${\left(x + 2\right)}^{2} + {\left(y\right)}^{2} = {\left(x - 8\right)}^{2}$

${x}^{2} + 4 x + 4 + {y}^{2} = {x}^{2} - 16 x + 64$

${y}^{2} = - 20 x + 60 = - 20 \left(x - 3\right)$

graph{y^2=-20(x-3) [-3.82, 7.28, -2.44, 3.107]}