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    love19890007's Avatar
    love19890007 Posts: 1, Reputation: 1
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    #1

    Dec 14, 2010, 06:42 AM
    how do I find the equation of a parabola given focus (-2,3) & directrix -3?
    galactus's Avatar
    galactus Posts: 2,271, Reputation: 282
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    #2

    Dec 14, 2010, 07:26 AM

    I assume the directrix is at y=-3?

    If so, the vertex lies on the x axis (why?).

    This is because the distance between the focus and the vertex is the

    same as the distance between the directrix and the vertex. Designate

    this distance between the vertex and directrix or between vertex and focus by 'p'.

    Thus, the distance between the focus and the directrix is 2p.

    Since it opens up the positive y axis, it has an equation of the form:



    Where (h,k) is the coordinates of the vertex.
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