F(0,-1), a point on the parabola is (2,-1). If the focus is 1 unit below the vertex, then the directrix is 1 unit above the vertex or y=1. It's a downward opening parabola where the vertex is the maximum point. Go to the right of the focus to a distance equal to 2, since the distance to the directrix = 2, to get the point on the parabola (2,-1)
plug it into the general equation for a parabola at the origin:
y=ax^2
-1=a(2)^2
a = -1/4
y=(-1/4)x^2 or
4y=-x^2
another way to find a is a=1/4p where y=(1/4p)x^2 where the focus is (0,p)=(0,-1). p=-1, so a=1/4p = -1/4
b) focus = (0,3) directrix is y=-3, find a point to the right of the focus on the parabola (6,3) plug it into the general equation for a parabola with vertex at the origin. It's an upward opening parabola.
y=ax^2
3=a(6)^2
a = 3/36 = 1/12
y=(1/12)x^2
12y = x^2
