Question

In Problems5–7, convert the polar equation to a rectangular equation. Graph the equation.

$r=7$

Short answer

The rectangular equation is $x^2+y^2=49$.

The graph is as follows,

Step-by-step solution

Step 1. Given information 

We are given a polar equation,

$r=7$

We have to convert the polar equation to a rectangular equation.

Step 2. Converting the polar equation to rectangular equation

We know that,

$$\begin{gathered} x=r\cos \theta \text{and} \\ y=r\sin \theta \\ {x}^2+y^2=r^2 \end{gathered}$$

So,

$r=7$

Squaring both sides, we get

$r^2=7^2$

$x^2+y^2=49$

Hence, the graph of $r=7$is a circle centre at origin and with radius equal to$7$.

Step 3. Graphing the equation

The graph is as follows,