Chapter 13.1, Problem 18WE

To determine

To find the center and radius of a circle

Answer to Problem 18WE

The value of center are $\left(-7,8\right)$ and radius are $\frac{6}{5}$

Explanation of Solution

The given equation is

  ${\left(x+7\right)}^2+{\left(y-8\right)}^2=\frac{36}{25}$

Calculation:

The center and radius of a circle can be obtained as

  ${\left(x+7\right)}^2+{\left(y-8\right)}^2=\frac{36}{25}$

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

Comparing given equation to the standard form of the equation

  $a=-7,b=8\text{ and }r=\frac{6}{5}$

Hence,

The value of center are $\left(-7,8\right)$ and radius are $\frac{6}{5}$