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Question 498546: x2 − 2y = 8x −10 what is the focus and focus width of this parabola?
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! x2 − 2y = 8x −10 what is the focus and focus width of this parabola?
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x2 − 2y = 8x −10
2y=x^2-8x+10
complete the square
2y=(x^2-8x+16)+10-16
2y=(x-4)^2-6
(x-4)^2=2y+6=2(y+3)
(x-4)^2=2(y+3)
Standard form for equation of this parabola: (x-h)^2=4p(y-k), (h,k) being the (x,y) coordinates of the vertex and parabola opens upwards.
For given equation of parabola:
vertex: (4,-3)
axis of symmetry: x=4
4p=2
p=2/4=1/2
focus: (4, 5/2)
focal width: 4p=2
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