Question

hoose ,begin emphasis,all,end emphasis, of the equations which represent the parabola with vertex the point negative 4 comma negative 6 and directrix y equals negative 2.

Answer options with 6 options
A.
left-parenthesis x plus 4 right-parenthesis squared equals negative 8 left-parenthesis y plus 4 right-parenthesis

B.
left-parenthesis x plus 4 right-parenthesis squared equals negative 16 left-parenthesis y plus 6 right-parenthesis

C.
left-parenthesis x plus 6 right-parenthesis squared equals negative 16 left-parenthesis y plus 4 right-parenthesis

D.
8 y equals negative x squared minus 8 x minus 48

E.
16 y equals negative x squared minus 12 x minus 100

F.
16 y equals negative x squared minus 8 x minus 112

Answer 1

Vertex (h,k)=(-4,-6). Directrix y=-2 is 4 units above the vertex, so p = -4 and 4p = -16. Standard form:
(x+4)^2 = -16(y+6) — option B.

Expanding: (x+4)^2 = -16(y+6) → x^2+8x+16 = -16y-96 → 16y = -x^2 -8x -112 — option F.

Answer: B and F.