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Question 581360: What is the focus of this parabola?
X^2 + 12X - 24Y + 84 = 0
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! What is the focus of this parabola?
X^2 + 12X - 24Y + 84 = 0
complete the square
(x^2+12x+36)-24y+84-36=0
(x+6)^2-24y+48=0
(x+6)^2=24y-48
(x+6)^2=24(y-2)
This is an equation of a parabola which opens upwards of the standard form: (x-h)^2=4p(y-k), (h
For given equation:
vertex: (-6,2)
axis of symmetry: x=-6
4p=24
p=6
x-coordinate of focus=-6
y-coordinate of focus=8 (p units above the vertex on the axis of symmetry)
focus: (-6,8)
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