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Tricky Parametric equation

  1. Jul 8, 2006 #1
    I would like to convert these parametric equations into a single
    f(x,y) = 0 function.

    X(t) = t^2 + t + 1
    Y(t) = t^2 - t +1

    In fact, what stops me is the imaginary roots of the parametric polynomials.

    Is there a way to get around the seemingly impossible explicit solving of the quadratics to isolate either X or Y ?
  2. jcsd
  3. Jul 8, 2006 #2


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    Note that x - t = y + t (or just subtract y(t) from x(t)).
    Last edited: Jul 8, 2006
  4. Jul 8, 2006 #3
    First note that X - Y = 2t, but also notice that these are both quadratic equations so you can solve one of them or the other to find t in terms of X or Y and then substitute this into X - Y = 2t or the equation for the other variable.
  5. Jul 8, 2006 #4


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    You just want to substitute t = (x - y) / 2. There's no need to solve any quadratics.
  6. Jul 9, 2006 #5
    Darn, I guess I should have seen that since I did notice that x - y = 2t.
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