## Precalculus (6th Edition) Blitzer

We know that for a circle, the standard form is ${{\left( x-h \right)}^{2}}+{{\left( y-k \right)}^{2}}={{r}^{2}}$, where the center is $\left( h,k \right)$ and the radius is $r$. So, the equation can be written as: \begin{align} & {{x}^{2}}+{{y}^{2}}-6y-7=0 \\ & {{x}^{2}}+\left( {{y}^{2}}-6y \right)=7 \\ & {{x}^{2}}+\left( {{y}^{2}}-6y+9 \right)=7+9 \\ & {{\left( x-0 \right)}^{2}}+{{\left( y-3 \right)}^{2}}=16 \end{align} So, the equation of the circle in the standard form is: ${{\left( x-0 \right)}^{2}}+{{\left( y-3 \right)}^{2}}={{4}^{2}}$ Now, compare this equation to the standard form, to get the value of $h=0,k=1\,,\,\text{ and }\,\,r=4$. Therefore, the center is $\left( 0,3 \right)$ and the radius is $4$ units.