Question

Find the standard form of the equation of the parabola with a focus at (0, -9) and a directrix y = 9.

Answer 1

use this.. (x - h)^2 = 4p(y - k)

Answer 2

4p?

Answer 3

1st the directrix is above the focus... so the parabola is concave down.

next the distance between the focus and directrix is twice the focal length... a



the focal length a = 9.

the vertex is a units above the focus

so the vertex is (0, -9 + 9)

so the vertex of the parabola is at (0,0)

so using the vertex form where (h, k) is the vertex and a is the focal length

\[(x - h)^2 = 4a(y - k)\]

substituting you get

\[(x - 0)2 = 4 \times 9 (y - 0)\]

or

\[x^2 = 36y\]

yo get it into standard from just make y the subject.

hope it helps