Question 39732
Okay from
3x + y^2 + 8y + 4 = 0 
we rearrange terms correctly and get
y^2 + 8y = -3x - 4
now complete the square
y^2 + 8y + 16 = -3x - 4 + 16
(y + 4)^2 = -3x + 12
(y + 4)^2 - 12 = -3x
x = (-1/3)(y + 4)^2 + 4
vertex is at (4, -4)
line of sym is y = -4
and since a = 1/4p and a = -1/3
p = |-3/4| = 3/4
focus is at (13/4, -4)
directrix at x = 19/4