# Standard form of a parabola with a vertex and directrix

Asked Nov 22, 2010, 04:21 PM — 1 Answer
Write the standard form of the parabola with its vertex at (0,0) at te origin and directrix x= -3

 galactus Posts: 2,272, Reputation: 1436 Ultra Member #2 Nov 23, 2010, 04:40 AM
Since the directrix is at x=-3, the parabola open toward the positive x-axis and has the equation

$y^{2}=4px$

The distance from the vertex to the directrix is the same as the distance from the vertex to the focus. P is this distance in the above equation. We can easily see that p=3.

Plug in p=3:

$y^{2}=12x$

That's it.

There are many parabola-related posts on this site. Do a search.

## Check out some similar questions!

(x-9)^2=-(y+8)?

What is the equation of a parabola with a vertex at (4,8) and a directrix at y=5? I calculated the distance from the vertex to the directrix as p=3. My answer key says p=6. I cannot see were I went wrong. Can anyone provide some guidance? If p=3 is correct then the equation would be: ...

Vertex, focus, and directrix of parabola [ 2 Answers ]

How do I find the vertex, focus, and directrix of a parabola?

Find the Vertex, Focus, Directrix of the parabola equation: X-(y^2)+4y-2=0