Chapter 9.2, Problem 19AYU

In Problems 15-30, transform each polar equation to an equation in rectangular coordinates. Then identify and graph the equation.

$r\cos \theta =-2$

To determine

To find: Transform the polar equation $r \text{cos}\theta = - 2$ to rectangular coordinates. Then identify and graph the equation.

Answer to Problem 19AYU

Solution

The graph of $r \text{cos}\theta = - 2$ is a vertical line with 2 units left to the line.

Given:

It is asked to transform the polar equation $r \text{cos}\theta = - 2$ to rectangular equation and graph it.

Explanation of Solution

Convert the polar equation to a rectangular equation.

$\begin{array}{c}r \text{cos}\theta = - 2\\ \left(x, y\right)=\left(r \text{cos}\theta , r \text{sin}\theta \right)\\ x = - 2\end{array}$

The graph of $r \text{cos}\theta = - 2$ is a vertical line with 2 units left to the line.

To sketch:

$r \text{cos}\theta = - 2$