Chapter 10, Problem 29RE

To determine

To graph: Analyze the equation and graph it.

Answer to Problem 29RE

Explanation of Solution

Given:

$r=\frac{8}{4+8\text{cos}\theta }$

Graph:

The graph of $r=\frac{8}{4+8\text{cos}\theta }$.

$r=\frac{8}{4+8\text{cos}\theta }$ can be rewritten as $r=\frac{2}{1+2\text{cos}\theta }$ is of the form $r=\frac{ep}{1+e\text{cos}\theta }$.

$ep=2$, $e=2, p=1$

Since $e=2$ and $p=2$, the curve represents a hyperbola and the directrix is perpendicular to the polar axis 1 unit right of the pole. Vertices are represented by$\left(\frac{2}{3},0\right)\text{ and} \left(-2,\pi \right)$, the center$\left(\frac{4}{3},0\right)$. The directrix, vertex is shown in the graph.