Chapter 9, Problem 5CT

To determine

The rectangular equation of polar equation $r=7$ and graph the equation.

Answer to Problem 5CT

Solution:

The rectangular equation of polar equation $r=7$ is $x^2+y^2=49$ .

The graph of polar equation $r=7$ is,

  

Explanation of Solution

Given information:

The polar equation, $r=7$

Consider the equation $r=7$ ,

Squaring on both sides of above equation.

  $\Rightarrow r^2=49$ .

In polar coordinates $x=r\cos \theta ,y=r\sin \theta$ and $r^2=x^2+y^2$ .

Substitute the value of $r^2$ in $r^2=49$

  $\Rightarrow x^2+y^2=49$ .

Therefore, the equation in rectangular coordinates is $x^2+y^2=49$ .

This is the equation of circle with center as origin and radius, $r=7$ .

The graph of polar equation $r=7$ is,