# How do you write an equation for the parabola with focus (0,2) and directrix y=-2?

Jan 25, 2016

$y = \frac{1}{8} {x}^{2}$

#### Explanation:

The equation of the parabola with focus and directrix - F(a, b), D(y=c)
is given by:
${\left(x - a\right)}^{2} + {b}^{2} - {c}^{2} = 2 y \left(b - c\right)$
Now substitute$F \left(0 , 2\right)$ and $D \left(x , - 2\right) \forall x : y \left(x\right) = c$
${x}^{2} = 2 y \left(2 - \left(- 2\right)\right) = 8 y$
$y = \frac{1}{8} {x}^{2}$