# What is the equation of the parabola with a vertex at (0,0) and a focus at (0,-3)?

##### 2 Answers

Jul 21, 2017

#### Explanation:

As vertex is

As every point on parabola is equidistant from focus and directrix, and the equation would be

or

or

or

graph{(12y+x^2)(x^2+y^2-0.02)(x^2+(y+3)^2-0.01)(y-3)=0 [-10, 10, -5, 5]}

Jul 21, 2017

#y=-x^2/12#

#### Explanation:

Given -

Vertex

Focus

This parabola opens down. Look at the graph -

So the equation of the parabola in such cases is

#x^2=-4ay#

Where

It is the distance from the vertex to focus.

Then -

#x^2=-4 xx 3 xx y#

#x^2=-12y#

#-12y=x^2#

#y=-x^2/12#