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Math Help - Parabola directrix

  1. #1
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    Parabola directrix

    I need to find the directrix of the parabola 12(y+4)=(y-6)^2.
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  2. #2
    Senior Member ecMathGeek's Avatar
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    Quote Originally Posted by amanda1 View Post
    I need to find the directrix of the parabola 12(y+4)=(y-6)^2.
    I'm guessing the equation should be:
    12(y + 4) = (x - 6)^2

    The directrix of a parabola is a distance "p" from the vertex of the parabola (h,k) away from the direction that the parabola opens.

    The standard form of the equation of a parabola is:
    4p(y - k) = (x - h)^2

    So, to find p, we set 12 equal to 4p:
    p = 3

    In this case, the parabola opens up, so the directrix is p = 3 units below the vertex (6,-4), along the line:
    y = -7
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