$$x^{2}+2(k+1)r+k=0$$
$\left\{\begin{matrix}k=-\frac{x^{2}+2r}{2r+1}\text{, }&r\neq -\frac{1}{2}\\k\in \mathrm{R}\text{, }&r=-\frac{1}{2}\text{ and }|x|=1\end{matrix}\right.$
$\left\{\begin{matrix}r=-\frac{x^{2}+k}{2\left(k+1\right)}\text{, }&k\neq -1\\r\in \mathrm{R}\text{, }&k=-1\text{ and }|x|=1\end{matrix}\right.$
