Chapter 13.1, Problem 22WE

To determine

To find the equation of the circle

Answer to Problem 22WE

The equation of the circle are $x^2+y^2=36$

Explanation of Solution

The given center and radius is

  $C\left(0,0\right);r=6$

Calculation:

The equation of the circle can be obtained as

The standard form of the equation of a circle with center and radius is

  ${\left(x-a\right)}^2+{\left(y-b\right)}^2=r^2$

Where $\left(a,b\right)$ is the center and r is the radius

So, the center $\left(a,b\right)=\left(0,0\right)\text{ and radius }\left(r\right)=\left(6\right)$

Put the values of $a=3,b=0\text{ and }r=8$ on the standard form of the equation

  $\begin{array}{l}{\left(x-0\right)}^2+{\left(y-0\right)}^2={\left(6\right)}^2\\ x^2+y^2=36\end{array}$

Hence,

The equation of the circle are $x^2+y^2=36$