Chapter 9.5, Problem 82E

To determine

To calculate: To describe the graph of the polar equation and then find the correspondingrectangularequation and sketch its graph

Answer to Problem 82E

The rectangular equation is $x^2+y^2=64$

Explanation of Solution

Given information: Polar equation is $r=8$

Formula Used:

Polar coordinate of a point $\left(r,\theta \right)$ in rectangular form is given as

  $\begin{array}{l}x=r\cos \theta \\ y=r\sin \theta \end{array}$

Where,

  $\begin{array}{l}{r}^2=x^2+y^2\\ \theta ={\tan }^{-1}\frac{y}{x}\end{array}$

Calculation:

Polarequation is given as

  $r=8$

The graph of the polar equation consists of all the points that are eight units away from the pole

Converting the polar equation into rectangular equation:

  $r=8$

Squaring both sides,

  $\begin{array}{l}{r}^2=8^2\\ r^2=64\end{array}$

Substituting $r^2=x^2+y^2$ and $r\cos \theta =x;r\sin \theta =y$ in above equation:

  $x^2+y^2=64$

Thus, rectangularequation is $x^2+y^2=64$

Graph of the above equation is

  

Conclusion:

Hence, rectangular equation is $x^2+y^2=64$