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Question 766197: What is the focus, vertex and directrix of the parabola
-2x^2+16x+24y-224=0....
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! What is the focus, vertex and directrix of the parabola
-2x^2+16x+24y-224=0..
complete the square
-2(x^2-8x+16)+24y=224-32
-2(x-4)^2=-24y+192
divide by -2
(x-4)^2=12y-96
(x-4)^2=12(y-8)
This is a parabola that opens upward.
Its basic form of equation: (x-h)^2=4p(y-k), (h,k)+(x,y) coordinates of the vertex
For given parabola:
vertex: (4,8)
axis of symmetry: x=4
4p=12
p=3
focus: (4,11) (p-units above vertex on the axis of symmetry)
directrix: y=5 (p-units below vertex on the axis of symmetry)
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