Answer
$r(t)= 3 \cos t \space i+3 \sin t \space j; 0 \leq t \leq 2 \pi$
Work Step by Step
Re-arrange the given equation as follows: $\dfrac{x^2}{9}+\dfrac{y^2}{9}=1$ ....(1)
Use Trigonometric identity such as: $\cos^2 t+\sin^2 t=1$ ...(2)
On comparing the both above equations (1) and (2), we have: $\cos^2 t=\dfrac{x^2}{9} \implies x=3 \cos t$
and $\sin^2 t=\dfrac{y^2}{9} \implies y =3 \sin t$
Therefore, $r(t)= 3 \cos t \space i+3 \sin t \space j; 0 \leq t \leq 2 \pi$
