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Math Help - How to find focus of parabola

  1. #1
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    How to find focus of parabola

    I have the equation: (y - 2)^2 = -8(x - 3)

    I learned that the focus is the "-8" part which is the distance from the vertex, and the vertex from the equation is (3,2) and this parabola is opening up sideways to the left. So from (3,2), the focus would be 8 units into the left direction which would be at (-5,2) but apparently this is wrong.

    How else would I find the focus?
    Last edited by daigo; June 13th 2012 at 04:43 AM.
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    Re: How to find focus of parabola

    Oh, never mind I forgot to factor out the '4' in the equation
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    Re: How to find focus of parabola

    Quote Originally Posted by daigo View Post
    I have the equation: (y - 2)^2 = -8(x - 3)

    I learned that the focus is the "-8" part which is the distance from the vertex
    Then you learned wrong! The focal length is "given by" that number but is not equal to it. If a parabola is given by (y- k)^2= 4p(x- h) then the focal length (distance from vertex to focus) is p. In your case, 4p= -8 so p= -2, not -8.

    , and the vertex from the equation is (3,2) and this parabola is opening up sideways to the left. So from (3,2), the focus would be 8 units into the left direction which would be at (-5,2) but apparently this is wrong.

    How else would I find the focus?
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