# How do you find the equation of a parabola with vertex at the origin and focus (-2,0)?

May 5, 2017

${y}^{2} = - 8 x$

#### Explanation:

As the vertex is $\left(0 , 0\right)$ and focus is $\left(- 2 , 0\right)$

We have axis of symmetry as $y = 0$ and directrix as $x = 2$.

As parabola is the locus of a point equidistant from focus $\left(- 2 , 0\right)$ and directrix $x = 2$, hence the equation of parabola is

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

or ${y}^{2} = - 8 x$

graph{(y^2+8x)((x+2)^2+y^2-0.02)(x-2)=0 [-10, 10, -5, 5]}