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)

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)