I have this example that I found quite easy

$\displaystyle r(t)= 4 \cos t i+5 \sin t j$

using $\displaystyle \cos^2t+\sin^2t= 1$ I concluded that

$\displaystyle 25x^2+16y^2=400$

But anyone shed some light on this one?

$\displaystyle r(t)= \frac{1-t^2}{1+t^2} i+\frac{2t}{1+t^2} j$