Question 614331: What is the vertex, focus, and directrix for this equation: (3x+6)^2=18y-36
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! What is the vertex, focus, and directrix for this equation:
(3x+6)^2=18y-36
expand
9x^2+36x+36=18y-36
divide by 9
x^2+4x+4=2y-4
(x+2)^2=2(y-2)
This is an equation of a parabola that opens upwards.
Its standard form: (x-h)^2=4p(y-k), (h,k)=(x,y) coordinates of the vertex
For given equation: (x+2)^2=2(y-2)
vertex: (-2,2)
axis of symmetry: x=-2
4p=2
p=1/2
focus: (-2,5/2) (1/2 unit above vertex on axis of symmetry)
directrix: y=3/2 (1/2 unit below vertex on axis of symmetry)
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