The focus of a parabola is (-4, -5), and its directrix is y = -1. What is the formula for the parabola in standard form.

Question

asked Mar 21, 2022 974 views

1 Answer

Marktucks · Answer 1 · 2022-03-28T01:07:56+0000

Answer:

(x - (-4))^2 = -8(y - (-3))

$Where\ p<0$

Explanation:

From the question we are told that:

Parabola focus co-ordinates

$F=(-4, -5)\\Directrix is y = -1$

Generally the equation for standard form of Parabola is mathematically given by

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

where p≠ 0

Generally the equation for Directrix of Parabola is mathematically given by

$y=k-p\\y=-1$

Generally the equation for Focus of Parabola F is mathematically given by

F=(h, k + p).

F=(-4, -5)

Therefore

k-p=-1

k=-1+p

Given

k+p=-5

-1+p+p=-5

2p=-4

p=-2

Therefore

k-p=-1

k-(-2)=-1

k=-3

Generally the equation for standard form of Parabola is mathematically given by

(x - (-4))^2 = 4(-2)(y - (-3))

(x - (-4))^2 = -8(y - (-3))

Where p<0