Write the equation of a parabola with the focus of (-2,4) and directrix y=2. Show your work including a sketch.

Airey
May 19, 2017

#1**+1 **

Since the vertex is halfway between the focus and the directrix, the vertex must be at (-2,3)

So....the distance between the vertex and the focus = 1 = p

So.....using 4py = (x - h)^2 + k where p = 1, h = -2 and k = 3

And we have

4(1)y = (x - -2)^2 + 3

4y = ( x + 2) ^2 + 3 multiply both sides by (1/4)

y = (1/4) ( x + 2)^2 + 3

Here's the graph : https://www.desmos.com/calculator/dfundaxw40

CPhill
May 19, 2017