Find the equation of a parabola with focus (2, - 3) and directrix x = 5.

Yay

directix x=5

that means the parabola opens left or right

the equation is

(y-h) ²=4p (x-h)

alrighty

vertex is (h, k)

p is distance from focus to vertex

also distance from vertex to directix

if p>0 then the parabola opens to the right and focus is to the right of directix

if p<0 then the parabola opens to the left and focus is to the left of directix

alrighty

the distance between directix and focus divided by 2=p

hmm, note which one is to the left or right of which

directix is x=5

focus is (2,-3) where x=2

focus is to the left of directix

alrighty

fro m 5 to 2 the distance is 3

3/2=1.5

and since the focus is to the left of the directix, it is - 1.5

so the parabols opens to the left

the vertex is 1.5 untis to the right of the focus

so vertex is at (3.5,-3)

so

equation is

(y - (-3)) ²=4 (-1.5) (x-3.5)

(y+3) ²=4 (-1.5) (x-3.5)