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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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Add and subtract 2, $y = \left(t+\frac1t\right)^2 - 2$. – Ishaan Singh Apr 15 '12 at 11:51
@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, – user21436 Apr 15 '12 at 13:00
up vote 2 down vote accepted

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

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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 $xt = t+1$. – heropup Jan 4 '14 at 19:04

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