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Math Help - Distance between vertices

  1. #1
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    Distance between vertices

    Determine the distance between the vertices of the hyperbola xy=8.

    I don't know how to do this one as it is a strange one. What happened to the x and y?

    Thanks.
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  2. #2
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    Did you graph y=8/x ?
    Draw the graph. Is it a hyperbola?
    What are the vertices?
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  3. #3
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    I believe a hyperbola opens either up/down or left/right. Y=8/x does not opens in this manner, it opens up like a reciprocal function.

    I'm not sure - this question comes under the hyperbola section. I'm suppose to calculate the vertices algebratically.
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  4. #4
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    Hello, shenton!

    Determine the distance between the vertices of the hyperbola xy = 8
    Evidently, you've never met this type of hyperbola.

    The graph looks like this:
    Code:
                              |
                              |*
                              |
                              | *
                              |  *
                              |    *
                              |        *
                              |              *
          - - - - - - - - - - + - - - - - - - - - -
               *              |
                     *        |
                         *    |
                           *  |
                            * |
                              |
                             *|
                              |
    The hyperbola is "tipped" at a 45 angle.
    The x- and y-axes are the asymptotes.

    The vertices lie on the line y = x.
    So we have: .x = 8 . . x = 2√2
    . . . . . . . . . . . . . . . _ . . ._ . . . - . . ._ . . . _
    The vertices are: .(2√2, 2√2) and (-2√2, -2√2)

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  5. #5
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    Thanks for the detailed explaination. Yes, I have never seen this type of hyperbola.

    I think I can work out the distance now.

    Given vertices (2√2, 2√2) and (-2√2, -2√2) of hyperbola xy=8:

    The distance is:

    √ [ (-2√2 - 2√2) + (-2√2 - 2√2) ]

    = √ [ (-4√2) + (-4√2) ]

    = √ (32 + 32)

    = √ 64

    = 8

    Thanks!
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