$\left\{\begin{matrix}c_{0}=\frac{x^{2}+y^{2}}{a^{2}}\text{, }&a\neq 0\\c_{0}\in \mathrm{C}\text{, }&\left(x=-iy\text{ or }x=iy\right)\text{ and }a=0\end{matrix}\right.$

$\left\{\begin{matrix}c_{0}=\frac{x^{2}+y^{2}}{a^{2}}\text{, }&a\neq 0\\c_{0}\in \mathrm{R}\text{, }&x=0\text{ and }y=0\text{ and }a=0\end{matrix}\right.$

$\left\{\begin{matrix}a=-c_{0}^{-\frac{1}{2}}\sqrt{x^{2}+y^{2}}\text{; }a=c_{0}^{-\frac{1}{2}}\sqrt{x^{2}+y^{2}}\text{, }&c_{0}\neq 0\\a\in \mathrm{C}\text{, }&\left(x=-iy\text{ or }x=iy\right)\text{ and }c_{0}=0\end{matrix}\right.$

$\left\{\begin{matrix}a=\sqrt{\frac{x^{2}+y^{2}}{c_{0}}}\text{; }a=-\sqrt{\frac{x^{2}+y^{2}}{c_{0}}}\text{, }&\left(x=0\text{ and }y=0\text{ and }c_{0}\neq 0\right)\text{ or }c_{0}>0\\a\in \mathrm{R}\text{, }&x=0\text{ and }y=0\text{ and }c_{0}=0\end{matrix}\right.$