Chapter 13.5, Problem 6ST1

To determine

To find: an equation of the circle

Answer to Problem 6ST1

The equation of the circle is

  ${\left(x+1\right)}^2+{\left(y-2\right)}^2=5^2$

Explanation of Solution

Given information: The center is $\left(-1,2\right)$ and the radius is $5$

Calculation:

  $\begin{array}{l}center\left(x_1,y_1\right)\text{ and radius }r\\ \Rightarrow {\left(x-x_1\right)}^2+{\left(y-y_1\right)}^2=r^2\\ \Rightarrow {\left(x-\left(-1\right)\right)}^2+{\left(y-2\right)}^2=5^2\\ \Rightarrow {\left(x+1\right)}^2+{\left(y-2\right)}^2=5^2\end{array}$