Question

Derive the equation of the parabola with a focus at (0, –4) and a directrix of y = 4. I understand a little bit of it, and... well, here is what I have so far...

(x-h)^2 = 4p(y-k)
h=0
k+p=-4
y=k-p=4

What's next?

Answer 1

@triciaal

Answer 2

from what you have h = 0 would mean x^2 = 4 p(y- k)

Answer 3

give me a few minutes to get the diagram

Answer 4

got it
take your time

Answer 5

" the equation of the parabola with focus (a , b) and directrix y = c is
(x-a)^2 + b^2 -c^2 = 2(b-c)y"

Answer 6

give it to me tomorrow, gtg

Answer 7

Let ( x0 , y0 ) be any point on the parabola. Find the distance between (x0 , y0) and the focus. Then find the distance between (x0 , y0) and directrix. Equate these two distance equations and the simplified equation in x0 and y0 is equation of the parabola.

Answer 8

distance between (x, y) and focus (0, -4) rt of (y + 4)^2 + x^2
distance between (x, y) and directrix = [y-4]
set them equal and square each side