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.
$\begin{array}{rcl} x=t + \frac{1}{t}, y= t^{2} + \frac{1}{t^{2}} \end{array}\qquad$
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.
$\begin{array}{rcl} x=t + \frac{1}{t}, y= t^{2} + \frac{1}{t^{2}} \end{array}\qquad$
Hint: compute $x^2$ and subtract $y$
$x=t+1/t$
$x^2=(t+1/t)^2$
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 $y=x^2-2$
$\begin{align} x&=t+1/t\\ xt-t&=1 \\ t(x-1)&=1\\ \\ t&=1/(x-1)\\ \\ y&=t^2+1/t^2\\ \\ y&=1/(x-1)^2 + (x-1)^2 \end{align}$