Chapter 11.3, Problem 37E

To determine

To determine: The find an appropriate window to produce the polar curve. Also, sketch the complete curve and identify the type of the curve.

Answer to Problem 37E

The curve is an ellipse.

Explanation of Solution

Given information:

The polar equation: $r=\frac{1}{1-0.8\cos \theta }$

Calculation:

The given equation is $r=\frac{1}{1-0.8\cos \theta }$ .

From the above equation, it is seen that $\left|r\right|=\left|\frac{1}{1-0.8\cos \theta }\right|\le 4$ .

So, consider the point $\left[-4,4\right]$ for y -range and $\left[-6,6\right]$ for the x -range.

The graph of the curve is shown below:

  

From the above graph, it is seen that the curve is an ellipse.