How do I change this parametric equation: $x=t+1/t, y=t^2 + 1/t^2$ into a Cartesian equation?

Question

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.

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

@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, — , Apr 15 '12 at 13:00

score 2 · Accepted Answer · answered Apr 15 '12 at 11:51

2

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

answered Apr 15 '12 at 11:51

Raymond Manzoni

score 2 · Answer 2 · edited Jul 31 '17 at 02:40

2

$$x=t+1/t$$

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

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 $y=x^2-2$

edited Jul 31 '17 at 02:40

user3658307

answered Jul 31 '17 at 02:01

Emma

score -2 · Answer 3 · edited Jan 04 '14 at 19:05

-2

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

edited Jan 04 '14 at 19:05

K. Rmth

answered Jan 04 '14 at 18:58

Helen

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 04 '14 at 19:04

3 Answers3