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Math Help - direct variation

  1. #1
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    direct variation

    given
     x^2 - y^2 \varpropto x^2 + y ^2
    prove that
    (a)
    y\varpropto  x
    (b)
    x-y  \varpropto x+ y
    ------------------------------------------------------
    (a)
    x^2 - y^2 = k (x^2 + y^2)
    (1-k)x^2 = (k+1)y^2
    x = \sqrt{\frac{k+1}{1-k}}y
    y\varpropto  x


    (b)
    x^2 - y^2 = k (x^2 + y^2)
     (x-y)(x+y) = k ((x+y)^2 - 2xy)
     x-y =k(x+y - \frac {2xy}{x+y})
    ???????????
    ??????????????????

    Thanks in advance.
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  2. #2
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    Add y on both side and subtract y on both side and find (x+y) and (x-y) and take the ratio of (x+y)/(x-y).
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  3. #3
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    x = \sqrt {\frac {k+1}{1-k}}y
    x+y = \sqrt {\frac {k+1}{1-k}}y+y
    x+y =( \sqrt {\frac {k+1}{1-k}}+1)y

    Cannot get it
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  4. #4
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    anybody please help?
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  5. #5
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    x+y = \sqrt\frac{1+k}{1-k}y + y

    x-y = \sqrt\frac{1+k}{1-k}y - y

    \frac{(x+y)}{(x-y)} = \frac{\sqrt\frac{1+k}{1-k} + 1 }{\sqrt\frac{1+k}{1-k} - 1}
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