Question

HELP PLEASE I NEED TO PASS THIS CLASS , I don' t understand this can someone please help me ?

The focus of the parabola is (3,-7) and the directrix is y= -4
What is an equation of the parabola ?
Options
A) (x -3)^2 = -3(y + 10)

B) (x -3)^2 = -1.5(y + 5.5)

C) (x -3)^2 = -12(y + 10)

D) (x -3)^2 = -6(y + 5.5)

Answer 1

y=-4
compared to focus
(3,-7)
vertex is in middle
so

-4 and -7, the average is -5.5
so vertex is (3,-5.5)
and distance from vertex to focus is from -5.5 to -7 or 1.5
focus is below vertex is p is negative


(x-3)^2=4(-1.5)(x+5.5)
(x-3)^2=-6(x+5.5)
D is answer