Answer:
(x-4)^2=-8(y-3)
This is a parabola.
Step-by-step explanation:
Since the directrix is horizontal, the parabola faces up or down. Since the focus is below the directix it faces down. This means p will be negative in the equation (x-h)^2=4p(y-k).
p also tells us the half the distance between the focus and the directrix. The distance between 1 and 5 is 4, so p=-2.
The vertex is half way point between focus (4,1) and directrix y=5.
So the vertex is (4, [1+5]/2 )= (4 ,6/2)=(4,3). This is (h,k) in our equation.
(x-h)^2=4p(y-k)
(x-4)^2=4×-2(y-3)
(x-4)^2=-8(y-3)
