# How do you find the equation in standard form of the parabola with directrix x=5 and focus (11, -7)?

Jul 21, 2018

The equation is $= x = \frac{1}{12} {\left(y + 7\right)}^{2} + 8$

#### Explanation:

Any point $\left(x , y\right)$ on the parabola is equidistant from the directrix and from the focus

$\left(x - 5\right) = \sqrt{{\left(x - 11\right)}^{2} + {\left(y + 7\right)}^{2}}$

Squaring both sides

${\left(x - 5\right)}^{2} = {\left(x - 11\right)}^{2} + {\left(y + 7\right)}^{2}$

${x}^{2} - 10 x + 25 = {x}^{2} - 22 x + 121 + {\left(y + 7\right)}^{2}$

$12 x = {\left(y + 7\right)}^{2} + 96$

$x = \frac{1}{12} {\left(y + 7\right)}^{2} + 8$

graph{(x-1/12(y+7)^2-8)=0 [-14.88, 50.06, -18.7, 13.76]}