Q. 46 - Calculus

Question

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

$r=\frac{2}{1+\cos \theta }$

Step-by-Step Solution

Answer

The graph will be 

Step 1. Given information.

The given equation is $r=\frac{2}{1+\cos \theta }$.

Step 2. Comparison.

On comparing the given equation,

$$\begin{gathered} r=\frac{eu}{1+e\cos \theta } \\ \text{The eccentricity }e=1 \\ \text{ Here }eu=2 \\ u=2 \end{gathered}$$

Step 3. Graph of the equation.

For $r=\frac{2}{1+\cos \theta }$ the eccentricity is $e=1$, so the graph is a parabola. The directrix will be the vertical line $x=2$.