Answer:
Correct option: First one -> [tex]x^2 = -12y[/tex]
Step-by-step explanation:
The focus and the vertex have the same x-coordinate, so we have a vertical parabola. The standard equation for this parabola is:
[tex]y = a(x-h)^2 + k[/tex]
If the vertex is at the origin, we have that:
[tex](h, k) = (0,0)\\h = 0, k = 0[/tex]
If the focus is at (0,-3), we have that:
[tex](h, k+p) = (0, -3)[/tex]
[tex]p = 1/4a[/tex]
[tex]k + p = -3[/tex]
[tex]1/4a = -3[/tex]
[tex]a = -1/12[/tex]
So we equation of the parabola is:
[tex]y = -x^2/12[/tex]
[tex]x^2 = -12y[/tex]
Correct option: First one
