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I've just started parametric equations on my own & I am a bit confused on how to convert this parametric equation into a Cartesian equation.

$\begin{array}{rcl} x=t + \frac{1}{t}, y= t^{2} + \frac{1}{t^{2}} \end{array}\qquad$

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    @IshaanSingh Please write those comments that answer a question as answer unless you think that the OP might have had something non-trivial to ask but turned out to be trivial because of a typo or other reasons why you think a comment is better than an answer. Here, I don't see any such--please correct me if I am wrong. Regards,2012-04-15

3 Answers 3

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Hint: compute $x^2$ and subtract $y$

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$x=t+1/t$

$x^2=(t+1/t)^2$

Expanding the perfect square $a^2+2ab+b^2$: $x^2=t^2+1/t^2+2$

As $y=t^2+1/t^2$, therefore $y=x^2-2$

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    Thanks for your answer. Please, however, [use MathJax/latex next time](https://math.meta.stackexchange.com/questions/5020/mathjax-basic-tutorial-and-quick-reference) :)2017-07-31
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$\begin{align} x&=t+1/t\\ xt-t&=1 \\ t(x-1)&=1\\ \\ t&=1/(x-1)\\ \\ y&=t^2+1/t^2\\ \\ y&=1/(x-1)^2 + (x-1)^2 \end{align}$

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    Your solution is not correct: the very first step is wrong. If $x = t + 1/t$, then multiplying both sides by $t$ gives $xt = {\color{red}{t^2}} + 1$, not $xt = t+1$.2014-01-04