Question

The focus of a parabola is (-4, -5), and its directrix is y = -1. Fill in the missing terms and signs in the parabola's equation in standard form.

Answer 1

Answer:

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

Step-by-step explanation:

Given:

focus of parabola=(-4,-5)

directrix= -1

Standard form of parabola :

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

where focus is:

(h, k + p)

directrix  is :

y = k - p

Now equating the values we get

(-4,-5) = (h,k+p)

h=-4

k+p=-5

k=-5-p

Also

y=-1 and y=k-p

i.e. k-p=-1

Substituting k=-5-p in above we get:

-5-p-p=-1

-2p=-1+5

p=4/-2

p=-2

Putting p=-2 in k-p=-1 we get:

k=-1-2

k=-3

Putting all the values in standard formula for parabola we get:

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

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