Chapter 13.1, Problem 24WE

To determine

To find the equation of the circle

Answer to Problem 24WE

The equation of the circle are ${\left(x+2\right)}^2+{\left(y-5\right)}^2=\frac{1}{9}$

Explanation of Solution

The given center and radius is

  $C\left(-2,5\right);r=\frac{1}{3}$

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 $\left(a,b\right)=\left(-2,5\right)\text{ and radius }\left(r\right)=\left(\frac{1}{3}\right)$

Put the values of $a=-2,b=5\text{ and }r=\frac{1}{3}$ on the standard form of the equation

  $\begin{array}{l}{\left(x-\left(-2\right)\right)}^2+{\left(y-5\right)}^2={\left(\frac{1}{3}\right)}^2\\ {\left(x+2\right)}^2+{\left(y-5\right)}^2=\frac{1}{9}\end{array}$

Hence,

The equation of the circle are ${\left(x+2\right)}^2+{\left(y-5\right)}^2=\frac{1}{9}$