Question

Derive the equation of the parabola with a focus at (−2, 4) and a directrix of y = 6. Put the equation in standard form.

Answer 1

Sketch a graph so you can find the vertex and determine if the parabola is horizontal or vertical. When i graph (-2,4) and then y=6, I find the middle is (-2,5) so that will be the vertex. The distance to the vertex is -1 so 4p=-4.
My formula is (x-h)^2=4p(y-k), now just plug in numbers. You should end up with (x+2)^2=-4(y-5).
Some instructors want you to write (y-k)=1/(4p)(x-h)^2 which is the same thing, so check to see which one you should be using.