Answer
The given statement is false. The correct statement is, “The graph of ${{\left( x-3 \right)}^{2}}+{{\left( y+5 \right)}^{2}}=36$ is the equation of a circle with radius 6 centered at $\left( 3,-5 \right)$.”
Work Step by Step
The standard equation of a circle that has center $\left( h,k \right)$ and radius $r$ is ${{\left( x-h \right)}^{2}}+{{\left( y-k \right)}^{2}}={{r}^{2}}$.
Write the standard form of the equation as shown below:
$\begin{align}
& {{\left( x-3 \right)}^{2}}+{{\left( y+5 \right)}^{2}}=36 \\
& {{\left( x-3 \right)}^{2}}+{{\left( y-\left( -5 \right) \right)}^{2}}={{6}^{2}}
\end{align}$
Comparing to the standard equation, we get $\left( h,k \right)=\left( 3,-5 \right)$ and the radius is 6.
Thus, the statement is false. The correct statement is, “The graph of ${{\left( x-3 \right)}^{2}}+{{\left( y+5 \right)}^{2}}=36$ is the equation of a circle with radius 6 centered at $\left( 3,-5 \right)$.”
