Chapter 9.1, Problem 40E

To determine

To draw: the polar equation.

Explanation of Solution

Given information:

The polar equation is $r=-1$ .

Graph: to draw the pattern, the solution to $r=-1$ are the ordered pairs $\left(r,\theta \right)$ where $r=-1$ and $\theta$ is any real number.

Some points are $\left(-1,0\right),\left(-1,\frac{\pi }{4}\right),\left(-1,\pi \right)$ .

The graph of the polar equation is the set of all ordered pairs of the form $\left(1,\theta \right)$ .

Any point that is $1$ units form the pole is included in this graph.

The graph is the circle at the origin with radius $1$ .

The graph can be obtained as:

  

Interpretation: from the above graph it can be observed that the type of curve of polar equation is circle.