Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

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.

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

share|improve this question
2  
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

2 Answers 2

up vote 1 down vote accepted

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

share|improve this answer

$$\begin{align} x&=t+1/t\\ xt-t&=1 \\ t(x-1)&=1\\ \\ t&=1/(x-1)\\ \\ y&=t^2+1/t^2\\ \\ y&=1/(x-1)^2 + (x-1)^2 \end{align}$$

share|improve this answer
1  
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 at 19:04

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.