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

${{\left( x-2 \right)}^{2}}+{{\left( y+5 \right)}^{2}}=9$ is $\left( f \right)$
The standard form of the equation of the circle centered at $\left( h,k \right)$ with the radius r is defined as, ${{\left( x-h \right)}^{2}}+{{\left( y-k \right)}^{2}}={{r}^{2}}$ Compare the provided equation with the standard form of the equation of the circle. It shows that the provided equation is the equation of a circle. The values of $h\text{ and }k$ are obtained as: \begin{align} & x-h=x-2 \\ & -h=-2 \\ & h=2 \end{align} And, \begin{align} & y-k=y+5 \\ & -k=5 \\ & k=-5 \end{align} So, the centre of the circle is obtained as $\left( 2,-5 \right)$. Therefore, the correct match for the graph of the equation ${{\left( x-2 \right)}^{2}}+{{\left( y+5 \right)}^{2}}=9$ is part (f).