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Question 39732: I tried to solve this problem but I am not sure about my answer. The thing is, I solved it by following the examples given by the book but I don;t really understand the principle behind.
Find the vertex,focus and directrix of the parabola in the given equation:
3x + ysquare + 8y + 4 =0
y square -8y = -3x + 4
2(y square -4y +8 ) = -3x + 4 + 8
2(y square - 2) square = -3 (x + 4)
( y - 2) square = - 3/2 ( x + 4)
Vertex = 2, -4
4p= -3/2
p= - 3/8
Focus -4 + (3/8), 2 = 35/8, 2
directrix = X = -4 - (-3/8) = - 29/8
Answer by fractalier(6550)   (Show Source):
You can put this solution on YOUR website! 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
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