Answer
$$r(t)=\lt 9+2\cos t, -4+3\sin t,0\gt.$$
Work Step by Step
We know that the equation of the given ellipse centered at $(9,-4,0)$ is $$
\left(\frac{x-9}{2}\right)^{2}+\left(\frac{y+4}{3}\right)^{2}=1
$$
To parametrize the ellipse, we put $\frac{x-9}{2}=\cos t$ and $\frac{y+4}{3}=\sin t$. Thus, we have $x=9+2\cos t$ and $y=-4+3\sin t.$
That is,
$$r(t)=\lt 9+2\cos t, -4+3\sin t,0\gt.$$
