Write $x^2+y^2=25$ as a vector valued function

Question

How can I write $x^2+y^2=25$ as a vector valued function? At first, I tried letting $x=t$. Then, $y=\pm \sqrt{25-t^2}$.

So, $r(t)=t \hat{i}+ \sqrt{25-t^2}\hat{j}$

Would this be correct? What happens to the $\pm$?

Answer 1

$r(t)=5\cos t \hat{i}+5\sin t\hat{j}$, where $0\leq t < 2\pi$