Chapter 13.1, Problem 23WE

To determine

To find the equation of the circle

Answer to Problem 23WE

The equation of the circle are ${\left(x+4\right)}^2+{\left(y+7\right)}^2=25$

Explanation of Solution

The given center and radius is

  $C\left(-4,-7\right);r=5$

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 $\left(a,b\right)=\left(-4,7\right)\text{ and radius }\left(r\right)=\left(5\right)$

Put the values of $a=-4,b=-7\text{ and }r=5$ on the standard form of the equation

  $\begin{array}{l}{\left(x-\left(-4\right)\right)}^2+{\left(y-\left(-7\right)\right)}^2={\left(5\right)}^2\\ {\left(x+4\right)}^2+{\left(y+7\right)}^2=25\end{array}$

Hence,

The equation of the circle are ${\left(x+4\right)}^2+{\left(y+7\right)}^2=25$