# How do you find the equation of the parabola whose Focus (0,-1/4) and directrix (0,1/4)?

Nov 29, 2015

The vertex will lie halfway between the focus and directrix.

#### Explanation:

I think you meant to write that the directrix is $y = \frac{1}{4}$. Assuming that is true, then the directrix lies above the focus, so this parabola opens downward (concave down).

Vertex $= \left(0 , 0\right)$ which is halfway between the focus and directrix.

Distance between focus and vertex $p = \frac{1}{4}$

Coefficient $\left\mid a \right\mid = \frac{1}{4 \times \frac{1}{4}} = 1$

The sign on $a$ is negative , so $a = - 1$

Equation of parabola : $y = - {x}^{2}$

hope that helps!