Derive the equation of the parabola with a focus at (6,2) and a directrix of y=1

Distance from focus to vertex=distance from vertex to directix

from (6,2) to y=1, the distance is 1
the focus is 1/2 higher than the vertex
vertex=(6,1.5)

for
(x-h)^2=4p(y-k)
vertex=(h,k)
p=distance from vertex to directix

vertex=(6,1.5)
ditance=0.5

(x-6)^2=4(0.5)(y-1.5)
(x-6)^2=2(y-1.5) is the equation
or
y=0.5x^2-6x+19.5 or
y=0.5(x-6)^2+1.5

The answer is option c.