Answer
The given statement is does not make sense.
Work Step by Step
The standard form of a circle 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 $r$.
The given equation can be written as:
${{\left( x-\left( -1 \right) \right)}^{2}}+{{\left( y-5 \right)}^{2}}={{\left( 2\sqrt{-1} \right)}^{2}}$
Now, comparing the equation to the standard form, we get $\left( h,k \right)=\left( -1,5 \right)$ and $r=2\sqrt{-1}$.
The equation does not represent a circle. It represents a set of imaginary points.
Thus, the equation ${{\left( x+1 \right)}^{2}}+{{\left( y-5 \right)}^{2}}=-4$ cannot be used to identify the circle center and radius.
