Chapter 9 - Analytic Geometry - Section 9.7 Plane Curves and Parametric Equations - 9.7 Assess Your Understanding - Page 715: 42

$x=2cos(\frac{2\pi}{3}t), y=3sin(\frac{2\pi}{3}t)$ with $0\le t\le3$

Answer may vary. 1. Based on the given conditions, we can write $x=2cos(kt), y=3sin(kt)$ with $0\le t\le3$ 2. With $p=3$, we have $\frac{2\pi}{k}=3$ and $k=\frac{2\pi}{3}$ 3. Thus $x=2cos(\frac{2\pi}{3}t), y=3sin(\frac{2\pi}{3}t)$ with $0\le t\le3$