a) y=-3 is the directrix, which has the same distance to the origin as the focus. So the focus is (0,3). A point on the parabola is (6,3) as (6,3) is a distance 6 from the focus and also 6 from the directrix.

Plug (6,3), x=6 and y=3 into the general form of the parabola equation to solve for "a"

y=a(x-h)^2 + k where (h,k) is the vertex, and in this problem h=0, k=0

y=ax^2

3 =a(6)^2 = 36a

a = 3/36 = 1/13

y= (1/13)x^2 or

13y = x^2

b) y=1/2 is the directrix, focus is (0,1/2) a point on the parabola is (1,1/2)

1/2 =a(1)^2

a = 1/2

y=(1/2)x^2

2y = x^2