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Elimination math problem

  1. Sep 21, 2007 #1
    1. The problem statement, all variables and given/known data

    If x=2at/(1+t^2) and y=b(1-t^2)/(1+t^2), show that x^2/a^2+y^2/b^2=1

    3. The attempt at a solution

    I've tried squaring both equations: xt^2=4a^2t^2/(1+2t^2+t^4)


    Now I've tried adding x^2 and y^2: 4a^2t^2+b^2(1-2t^2+t^4)/(1+2t^2+t^4)

    Am I able to cancel any of this down now?
  2. jcsd
  3. Sep 21, 2007 #2


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    Try solving the y equation for t and substituting that t into the x equation.
  4. Sep 21, 2007 #3


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    I think you'll find it easier if you add x2/a2 to y2/b2.

    Its made fairly easy since the denominators are the same and thus its just a manipulation of the numerator.
  5. Sep 21, 2007 #4


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    First simplify each term x^2/a^2 and y^2/b^2.

    Then expand the numerator of y^2/b^2. Add it to x^2/a^2, which has the identical denominator.

    Can you get the rest?
    Last edited: Sep 21, 2007
  6. Sep 22, 2007 #5
    Oh yes thanks! x^2/a^2+y^2/b^2=4t^2+1-2t^2+t^4/1+2t^2+t^4
    So the left hand side cancels to give 1.
    Thanks again!
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