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Math Help - [SOLVED] affine geometry

  1. #1
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    [SOLVED] affine geometry

    hey all,
    i have been given this question and i dont have a clue where to start

    For any subset
    of the affine plane R2, let G() denote the group of all affine transformations

    f
    of R2 such that f() = .


    1)Find all the elements of the group G = G(), where is the hyperbola xy = 1

    in R2.

    thanks
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  2. #2
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    Jan 2009
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    Hey, how was this solved please? Thanks.
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  3. #3
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    i managed to do it myself in the end.

    you have the form xy=1.

    so using affine geometry you can also write this as
    x->Ax+b, where A is a 2x2 matrix with abcd as coefficients and uv as t
    then
    (ax+by+u)(cx+dy+v)=1
    now if you expand out and compare coefficients, you two cases.
    a=0 or c=0, follow through for this and you will get two matrices as your answer.
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