Answer
$(x-3)^2+(y-1)^2=4$; see figure.
Work Step by Step
Step 1. From the given equations, we have
$cos(t)=\frac{x-3}{2}$ and $sin(t)=\frac{y-1}{2}$
Step 2. Using the identify $sin^2t+cos^2t=1$, we have $(\frac{x-3}{2})^2+(\frac{y-1}{2})^2=1$ or $(x-3)^2+(y-1)^2=4$, indicating a circle centered at $(3,1)$ with radius $r=2$
Step 3. Given $0\leq t\lt 2\pi$, we can graph the above equation as shown in the figure.
