Question 1056881: Could someone explain to me how to find the equation of a parabola given the focus and directrix? Thanks a lot in advance!
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! find the equation of a parabola given the focus and directrix? Thanks a lot in advance!
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Let the focus be (4,6)
Let the directrix be the line y = -4
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The vertex is half-way from the directrix to the focus:
Vertex:: (4,1) = (h,k)
p is half the distance from the directrix to the focus::
p = 5
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Since that focus is above that directrix the parabola
opens upward from (4,1)
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Form:: (x-h)^2 = p(y-k)
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(x-4)^2 = 5(y-1)
5y - 5 = x^2 - 8x + 16
5y = x^2 - 8x + 21
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y = (1/5)x^2 - (8/5)x + (21/5)
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Cheers,
Stan H.
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