## Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Equation of a circle with center $\left( -3,5 \right)$ and radius $4$ is ${{\left( x+3 \right)}^{2}}+{{\left( y-5 \right)}^{2}}=16$
First we use the formula of circumference of a circle to calculate the radius, $C=2\pi r$. Put the value of circumference $8\pi$ in formula $C=2\pi r$. \begin{align} & 2\pi r=8\pi \\ & r=\frac{8\pi }{2\pi } \\ & r=4 \\ \end{align} Put the value of radius $4$ and center coordinate $\left( -3,5 \right)$ in the standard equation of the circle: \begin{align} & {{\left( x-h \right)}^{2}}+{{\left( y-k \right)}^{2}}={{r}^{2}} \\ & {{\left( x-\left( -3 \right) \right)}^{2}}+{{\left( y-\left( 5 \right) \right)}^{2}}={{\left( 4 \right)}^{2}} \\ & {{\left( x+3 \right)}^{2}}+{{\left( y-5 \right)}^{2}}=16 \end{align} Thus, the equation of the circle with center $\left( -3,5 \right)$ and radius $4$ is ${{\left( x+3 \right)}^{2}}+{{\left( y-5 \right)}^{2}}=16$.