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Math Help - Equation of a Parabola Given Vertex and Focus

  1. #1
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    Equation of a Parabola Given Vertex and Focus

    Hi--

    I have to write an equation of a parabola with vertex (0,-6) and focus (0,5). p = 11

    I have done it two ways and have gotten two different answers. I just need to know which one is correct.

    1. y=p(x-h)^2+k
    y=11(x-0)^2-6
    y=11x^2-6

    2. (x-h)^2=4p(y-k)
    (x-0)^2 = 4(11)(y+6)
    x^2 = 44(y+6)
    x^2=44y + 264
    x^2-264= 44y
    (x^2-264)/44=44y/44
    1/44x^2-6=y

    Could you let me know which one of these is the correct equation? Thanks.
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  2. #2
    A riddle wrapped in an enigma
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    Quote Originally Posted by Joanie View Post
    Hi--

    I have to write an equation of a parabola with vertex (0,-6) and focus (0,5). p = 11

    I have done it two ways and have gotten two different answers. I just need to know which one is correct.

    1. y=p(x-h)^2+k
    y=11(x-0)^2-6
    y=11x^2-6

    2. (x-h)^2=4p(y-k)
    (x-0)^2 = 4(11)(y+6)
    x^2 = 44(y+6)
    x^2=44y + 264
    x^2-264= 44y
    (x^2-264)/44=44y/44
    1/44x^2-6=y

    Could you let me know which one of these is the correct equation? Thanks.
    Hi Joanie,

    I'm going to go with door number 2.
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  3. #3
    MHF Contributor
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    Talking

    Quote Originally Posted by Joanie View Post
    1. y=p(x-h)^2+k
    Shouldn't the "p" actually be an "a"...?
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