Answer:
Step-by-step explanation:
We are given the directrix equation and the location of the focus as a means to determine what the vertex (h, k) of the parabola is. Since the directrix is a horizontal line AND since the directrix is below the focus, AND since the parabola ALWAYS wraps itself around the focus, this is a positive parabola of the form
[tex](x-h)^2=4p(y-k)[/tex]
We also know that since the vertex is directly in between the focus and the directrix, it has coordinates of (0, 0). So h = 0 and k = 0.
By definition, p is the distance between the vertex and the focus (and also the vertex and the directrix since they are both the same). Therefore, p = 4.
Filling in our equation with those values gives us
[tex]x^2=16y[/tex] and solving for y gives us
