Answer:
Since the focus is at (-6,-11) and the directrix is at y=9:
The vertex is halfway between the focus and the directrix, so the vertex is at (-6,-1). (Draw this on graph paper if that doesn't make sense.)
The general form (conics form) of a parabola: 4p(y-k)=(x-h)^2 (vertex is (h,k) and "p" is the distance between the focus and vertex (or between vertex and directrix)).
(h,k) = (-6,-1)
p = 10 (distance between focus and vertex), so 4p = 40.
Therefore:
40(y+1)=(x+6)^2
Or if you need to rearrange to "vertex form": y=(1/40)(x+6)^2 - 1
Step-by-step explanation:
