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    rathfam5's Avatar
    rathfam5 Posts: 1, Reputation: 1
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    #1

    Jun 28, 2009, 08:04 AM
    Find equation of a parabola given the vertex and directrix
    What is the equation of a parabola with a vertex at (4,8) and a directrix at y=5?

    I calculated the distance from the vertex to the directrix as p=3.
    my answer key says p=6. I cannot see were I went wrong. Can anyone provide some guidance?

    If p=3 is correct then the equation would be:

    Focus = (4,11)

    (x-h)^2 = 2p(y-k)

    (x-4)^2 = 6(y-8)

    Thanks in advance!
    galactus's Avatar
    galactus Posts: 2,271, Reputation: 282
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    #2

    Jun 28, 2009, 09:34 AM
    From what I can see, p=3. The vertex is halfway between the focus and the directrix.

    The distance between the focus and the directrix is 6, if they mean that.

    One thing, the formula is , not 2p.

    Since p=3, we get 4p=12. What you have looks good, other than that.

    I graphed it and here is what I got.
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