Answer
part $\left( e \right)$
Work Step by Step
The standard form of the equation of the circle centred 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 (e).
