Answer
$\frac{(x-1)^2}{9}+\frac{y^2}{4}=1$
See graph.
Work Step by Step
Step 1. Using the given equations, we have
$sin(t)=\frac{x-1}{3}$ and $cos(t)=\frac{y}{2}$
Step 2. Using the identify $sin^2t+cos^2t=1$, we have $(\frac{x-1}{3})^2+(\frac{y}{2})^2=1$ or $\frac{(x-1)^2}{9}+\frac{y^2}{4}=1$
Step 3. We can graph the ellipse as shown in the figure.
