Solve r^2*-a^2=b^2x+b^2+2ab

$$r ^ { 2 } \times - a ^ { 2 } = b ^ { 2 } x + b ^ { 2 } + 2 a b$$

Solve for a

$$\left\{\begin{matrix}a=\frac{b\left(-\sqrt{1-r^{2}-xr^{2}}-1\right)}{r^{2}}\text{; }a=\frac{b\left(\sqrt{1-r^{2}-xr^{2}}-1\right)}{r^{2}}\text{, }&r\neq 0\text{ and }x\leq -1+\frac{1}{r^{2}}\\a=\frac{b\left(-x-1\right)}{2}\text{, }&b=0\text{ or }r=0\\a\in \mathrm{R}\text{, }&r=0\text{ and }b=0\end{matrix}\right.$$

Solve for b

$$\left\{\begin{matrix}b=-\frac{a\left(\sqrt{1-r^{2}-xr^{2}}+1\right)}{x+1}\text{; }b=-\frac{a\left(-\sqrt{1-r^{2}-xr^{2}}+1\right)}{x+1}\text{, }&x\neq -1\text{ and }\left(r=0\text{ or }x\leq \frac{1-r^{2}}{r^{2}}\right)\\b=-\frac{ar^{2}}{2}\text{, }&a=0\text{ or }x=-1\\b\in \mathrm{R}\text{, }&x=-1\text{ and }a=0\end{matrix}\right.$$