# Thread: Find the equation for the parabola...

1. ## Find the equation for the parabola...

Find the equation for the parabola that has its focus on the positive x-axis, 4 units away from the directrix.

2. Hello, uselessjack!

There are four forms of the parabola, each with its own equation.

I'll derive one of them . . .

Find the equation for the parabola that has its focus on the positive x-axis,
4 units away from the directrix.
This is a "vertical" parabola, opening upward.

The focus is at $F(f,0)$
The directrix is: $y = -4$
Code:
            |
|
*   |                   *
|       F
- - -*- + - - - o - - - - -* - -
* |     (f,0)       *
*       :       *
|  *    :    *
|       o V
|     (f,-2)
|       :
|       :
- - - + - - - + - - - - -
-4|
|

The equation has the form: . $(x-h)^2 \:=\:4p(y-k)$

The vertex is at: . $V(f,-2)$

The value of $p$ is: . $p \,=\,2$

The equation is: . $(x-f)^2 \:=\:4(2)\left(y-[-2]\right) \quad\Rightarrow\quad (x-f)^2 \:=\:8(y+2)$

3. Thank you for your help and time. I am left with confusion still. I thought there would be a specific answer. I am given five choices and still can't figure out which one is correct.

4y^2 = 4x
y^2 = 4x
y^2 = 8x
x^2 = 16y
4y^2 = x