# Thread:

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!

Is there more information?
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

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