I am having difficulty determining the equation for a parabola when the focus is given, and the directrix is given.

For example, Focus at (-2, 2) and directrix y= -2. I believe I use the distance formula, however, the distance formula states you need to points X1, Y1, and X2, Y2. I am not given an additional point!

Help!

DiMathluv:eek:

No distance formula needed.

The directrix is at y = -2 and the focus at F(-2,2). That means the vertex is in between.

It is at V(-2,0).

Now, we can use (x-h)^{2}=4p(y-k)

Where p=\frac{1}{4a}

With h being the x-coordinate of the vertex and k the y-coordinate. It is h=-2 and k=0 and p=2

p is the distance between the focus and the vertex.

(x+2)^{2}=8(y-0)

Now, express in ax^{2}+bx+c format:

y=\frac{1}{8}x^{2}+\frac{1}{2}x+\frac{1}{2}

The directrix is at y = -4 and the focus at F(0,4). That means the vertex is in between.