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Algebra II

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Write an equation for the parabola with focus (1,3) and vertex (0,3).

I cannot find any example in my book that works a problem with the vertex, all of the examples that I have to go by give only the focus and directrix.

Thanks.

  • Algebra II - ,

    Since this parabola has vertex to the left and at the same level as the focus, it opens right and is of form:

    (y-k)^2 = 4 a (x-h)

    the vertex is at (h,k)
    distance from vertex to focus = a
    distance from vertex to directrix = a

    here, vertex at (0,3)
    so (y-3)^2 = 4 a (x)
    since a is distance from vertex to focus
    (y-3)^2 = 4*1 x = 4 x
    so
    x = (1/4)(y^2 - 6 y + 9)

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