SOLUTION: Please help me with this problem: Sketch the parabola whose equation is {{{x^2 - 8y - 4x + 20 = 0}}}. Determine the coordinates of the focus, the equation of the directrix, and the

Algebra ->  Finance -> SOLUTION: Please help me with this problem: Sketch the parabola whose equation is {{{x^2 - 8y - 4x + 20 = 0}}}. Determine the coordinates of the focus, the equation of the directrix, and the      Log On


   

Question 991911: Please help me with this problem: Sketch the parabola whose equation is x%5E2+-+8y+-+4x+%2B+20+=+0. Determine the coordinates of the focus, the equation of the directrix, and the length of the latus rectum of the parabola.
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Sketch the parabola whose equation is x%5E2+-+8y+-+4x+%2B+20+=+0. Determine the coordinates of the focus, the equation of the directrix, and the length of the latus rectum of the parabola.
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x^2 - 8y - 4x + 20 = 0
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8y = x^2 - 4x + 20
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8y = x^2-4x+4 + 16
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8y = (x-2)^2 + 16
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y = (1/8)(x-2)^2 + 2
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Vertex = (2,2)
4p = 1/8
p = 1/16
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Focus = (2,33/16)
Latus Rectum = 4p = 1/4
Directrix :: y = 2-(1/16) = 31/16
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graph%28400%2C400%2C-10%2C10%2C-10%2C10%2C%281%2F8%29%28x-2%29%5E2%2B2%29
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Cheers,
Stan H.
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