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Math Help - Find the vertex, focus, and directrix of the parabola x + y^2 = 0

  1. #1
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    Find the vertex, focus, and directrix of the parabola x + y^2 = 0

    The question asks me to find the vertex, focus, and directrix of the parabola:
    x + y^2 = 0

    I usually don't have problems with these types of questions, but this particular one is set up differently than the others that I have done.

    I am not sure how to do it. Can anyone help?
    Thanks.
    Last edited by mr fantastic; April 9th 2010 at 02:30 AM. Reason: Changed post title
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  2. #2
    A riddle wrapped in an enigma
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    Quote Originally Posted by iluvmathbutitshard View Post
    The question asks me to find the vertex, focus, and directrix of the parabola:
    x + y^2 = 0

    I usually don't have problems with these types of questions, but this particular one is set up differently than the others that I have done.

    I am not sure how to do it. Can anyone help?
    Thanks.
    Hi iluvmathbutitshard,


    x+y^2=0

    Put this in the form: x=a(y-k)^2+h


    x=-(y-0)^2+0

    Vertex is at (0, 0). Since a=-1, the parabola opens left.

    Focus is at \left(h+\frac{1}{4a}, k\right)

    Directrix is x=h-\frac{1}{4a}
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  3. #3
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    Thank you for answering. Is this correct?
    Vertex: (0,0)
    Focus: (-1/4, 0)
    Directrix: x = 1/4
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  4. #4
    A riddle wrapped in an enigma
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    Quote Originally Posted by iluvmathbutitshard View Post
    Thank you for answering. Is this correct?
    Vertex: (0,0)
    Focus: (-1/4, 0)
    Directrix: x = 1/4
    Looks good to me.
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