Chapter 10.1, Problem 45E

Suppose that the position of one particle at time t is given by

$\begin{array}{lll}{x}_1=3\sin t\hfill & y_1=2\cos t\hfill & 0\le t\le 2\pi \hfill \end{array}$

and the position of a second particle is given by

$\begin{array}{lll}{x}_2=-3+\cos t\hfill & y_2=1+\sin t\hfill & 0\le t\le 2\pi \hfill \end{array}$

1. (a) Graph the paths of both particles. How many points of intersection are there?
2. (b) Are any of these points of intersection collision points? In other words, arc the particles ever at the same place at the same time? If so, find the collision points,
3. (c) Describe what happens if the path of the second particle is given by

$\begin{array}{lll}{x}_2=3+\cos t\hfill & y_2=1+\sin t\hfill & 0\le t\le 2\pi \hfill \end{array}$