Chapter 10.3, Problem 36E

To determine

To find: The graph of the polar curve $r=\frac{12}{8+6\cos \theta }$ and identify the name of the curve.

Answer to Problem 36E

The graph of the curve is shown in Figure (1) and it is an ellipse.

Explanation of Solution

Given information: The given equation is $r=\frac{12}{8+6\cos \theta }$ .

Calculation:

To graph a function $r=\frac{12}{8+6\cos \theta }$ , follow the steps using graphing calculator.

First press $\boxed{\text{MODE}}$ key on graphical calculator and select the polar mode. Press $\boxed{\text{Y}=}$ key and enter right hand side of the equation after the symbol ${\text{Y}}_1$ . Enter the keystrokes $\boxed{\text{12}}\boxed{÷}\boxed{(}\boxed{8}\boxed{+}\boxed{6}\boxed{\text{COS}}\boxed{\theta }\boxed{)}\boxed{)}$ .

The display will show the equation,

  ${\text{r}}_{\text{1}}=12/\left(8+6\cos \left(\theta \right)\right)$

The appropriate viewing window for the function is $\left[-10,10\right]$ by $\left[-10,10\right]$ .

Now, press the $\boxed{\text{GRAPH}}$ key to produce the graph of given equation as shown in Figure (1).

  

Figure (1)

Thus, the graph of the curve is shown in Figure (1) and it is an ellipse.