Question

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

$r=\frac{5}{1+\cos \theta }$

Short answer

The graph is

Step-by-step solution

Step 1. Given information.

The given equation is$r=\frac{5}{1+\cos \theta }$.

Step 2. Comparison.

On comparing the given equation with standard form,

$$\begin{gathered} r=\frac{eu}{1+e\cos \theta } \\ \text{The eccentricity}e=1 \\ \text{Here}eu=5 \\ u=5 \end{gathered}$$

Step 3. Graph.

For $r=\frac{5}{1+\cos \theta }$the eccentricity is$e=1$, so the graph is a parabola. The directrix will be the vertical line $x=5$.