Provide an Appropriate Response $r = 1 + a \cos \theta$

Essay

Provide an appropriate response.
-Graph the equation $r = 1 + a \cos \theta$ for several values of a in order to get an idea of what these curves look like. (Try both $| \mathrm { a } | < 1$ and $| \mathrm { a } | > 1$ .) Show that the graph will have an inner loop for every a such that $| \mathrm { a } | > 1$ and find the values of $\theta$ that correspond to the inner loop.