Answer
${{\left( x-2 \right)}^{2}}+{{\left( y+5 \right)}^{2}}=9$ is $\left( f \right)$
Work Step by Step
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).
