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Math Help - removing parameter t to find the locus

  1. #1
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    Arrow removing parameter t to find the locus

    Find an equation connecting x and y, by removing the parameter t from the following:
     x = \frac{ct - \frac{c}{t^3}}{2}
     y=\frac{\frac{c}{t} - t^3c}{2}

    Thanks
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  2. #2
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    Quote Originally Posted by differentiate View Post
    Find an equation connecting x and y, by removing the parameter t from the following:
     x = \frac{ct - \frac{c}{t^3}}{2}
     y=\frac{\frac{c}{t} - t^3c}{2}

    Thanks
    1. Simplify:

     x = \frac{ct - \frac{c}{t^3}}{2}~\implies~x=\dfrac{c(t^4-1)}{2t^3}

     y=\frac{\frac{c}{t} - t^3c}{2}~\implies~y=\dfrac{c(1-t^4)}{2t}

    2. Then calculate

    \dfrac yx = -t^2

    3. Now continue!
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