8 PTS! In two or more complete sentences, Explain how you would find the equation of a parabola, given the coordinate of the focus and the equation of the directrix.

Yah it would a even number or something even i think

2 types of parabolas

left right or up down opening ones

left right ones are in form (y-k) ²=4p (x-h)

up down ones are (x-h) ²=4p (y-k)

in all of them, the vertex is (h, k)

p is the distance from the vertex to the focus, also the shortest distance from the vertex to the directix making p half of the distance of the shortest path from focus to directix

if p is positive, then the parabola opens up or right

if p is negative then the parabola opens down or left

if the directix is y=something, then it is a up down parabola

if directix is x=something, then it is a left right parabola

directix is outside the parabola, kind of at the back

so lets say we had

focus = (2,3) and directix is x=-4

dirextix is x = - 4 so left right

from x=-4 to x=2 (focus), that is distance of 6

6/2=3

p=3

wait, ok, so directix is on oposite side of opening

hmm, - 4 is to left of the 2 so

the direxix is at back so the parabola opens to the right

p=3, positive 3

then we have the vertex is halfway between those

so 3 back from focus is from (2,3) to (-1,3)

so vertex is (-1,3)

equation is

(y-3) ²=4 (3) (x - (-1))

(y-3) ²=4 (3) (x+1)