# How do you find the standard form of the equation of the parabola with a focus at (3, 0) and a directrix at x = -3?

Dec 9, 2016

THe equation of the parabola is ${y}^{2} = 12 x$

#### Explanation:

The vertex is midway between the focus ad the directrix

So, the vertex is $\left(0 , 0\right)$

Let $P = \left(x , y\right)$ be a point on the parabola.

The distance of P from the directrix is equal to the distance from the focus.

$x + 3 = \sqrt{{\left(x - 3\right)}^{2} + {\left(y - 0\right)}^{2}}$

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

${x}^{2} + 6 x + 9 = {x}^{2} - 6 x + 9 + {y}^{2}$

${y}^{2} = 12 x$

graph{y^2=12x [-10, 10, -5, 5]}