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vesna_86 [32]
3 years ago
12

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

Mathematics
2 answers:
kykrilka [37]3 years ago
4 0

Answer:

On edg. the answer is (y+3)^2 = -6(x- 7/2)

Step-by-step explanation:

wolverine [178]3 years ago
3 0
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)
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