Write the equations of these parabolas in vertex form: focus at (-5, -3), and directrix y = -6 focus at (10, -4), and directrix y = 6.

Step-by-step explanation:

focus at (-5, -3), and directrix y = -6

Directrix y=-6 so its  a vertical parabola

so equation is

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

(h,k) is the center

P is the distance between focus and vertex

distance between focus and directrix = 2p

distance between -3  and y=-6 is 3

2p = 3

p = 3/2 or p = 1.5

Focus is (h, k+p)

given focus is (-5, -3) so h= -5  and k+p = -3

k+p=-3, plug in 1.5 for p

k + 1.5 = -3

subtract 1.5 on both sides

k = -4.5

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

divide by 6 on both sides

then subtract 4.5 on both sides

focus at (10, -4), and directrix y = 6.

Directrix y=6 so its  a vertical parabola

so equation is

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

distance between focus and directrix = 2p

distance between -4  and y=6 is -4-6=-10

2p = -10

p = -5

Focus is (h, k+p)

given focus is (10, -4) so h= 10  and k+p = -4

k+p=-4, plug in 5 for p

k - 5 = -4

add 5 on both sides

k = 1

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

divide by -20 on both sides and add 1 on both sides