Question

Derive the equation of the parabola with a focus at (4, -7) and a directrix of y = -15. Put the equation in standard form.

Answer 1

So every point on the curve of the parabola will have the same distance from the focus as it will the directrix.
So find the distances between (x,y) and the focus.
Find the distance between that same (x,y) and the directrix.
Set those distances equal to each other.
Square both sides to get rid of the square roots.
Then you may want to do a bit of rearranging

Answer 2

first thing is to make sketch. Did you do that?

Answer 3

keep in mind that the vertex of the parabola will be between the focus point and the directrix

since the distance from the vertex to the focus is the same as the distance from the vertex to the directrix

so where do you think is the vertex?