Hello, Hockey_Guy14!

Determine an equation for the parabola with focus

and directrix

There are two types of parabola:

. .

where is the vertex

and is the distance from the vertex to the focus.

. . (It is also the distance from the vertex to the directrix.)

Graph the focus and directrix. Code:

* |
| * :
| * :
| F V :
- - + - - o - - * - - : -
| 3 5 :
| * :
| * x=7
* |

The vertex is midway between the focus and the directrix: .

. . And we see that: .

The parabola always "bends around" the focus

. . and "away from" the directrix.

This parabola opens to the left.

. Its equation is: .

Therefore, the equation is: .