Question

Use polar coordinates to graph the conics in Exercises 44–51.

$r=\frac{1}{1-\cos \theta }$

Short answer

The graph is

Step-by-step solution

Step 1. Given information.

The given equation is$r=\frac{1}{1-\cos \theta }$

Step 2. Comparison.

On comparing the equation to standard form $r=\frac{eu}{1+e\cos \theta }$,

$$\begin{gathered} \text{The eccentricity}e=1 \\ eu=1 \\ u=1 \end{gathered}$$

Step 3. Graph.

For$r=\frac{1}{1-\cos \theta }$the eccentricity is $e=1$, so the graph is a parabola. The directrix is perpendicular to the polar axis at a distance $u=\frac{2}{3}$units to the right of the pole. The directrix will be the vertical line $x=\frac{2}{3}$.