Question

The focus of a parabola is (3,−7) and the directrix is y=−4.

What is an equation of the parabola?

A) (x−3)2=−1.5(y+5.5)

B) (x−3)2=−12(y+10)

C) (x−3)2=−3(y+10)

D) (x−3)2=−6(y+5.5)

Answer 1

(x−3)2=−6(y+5.5)

Explanation:

I took the quiz

Answer 2

we know that
y=-4
compared to focus (3,-7)
vertex is in middle
so
(-4-7)/2----> -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
so
p is negative
is a vertical parabola open down

(x-3)²=4(-1.5)(y+5.5)(x-3)²=-6(y+5.5)

the answer is the option
D) (x−3)2=−6(y+5.5)