Question 123
Find all values of the parameter $a \in \mathbb{R}$ for which the system
$$
\left\{\begin{array}{c}
\sqrt{x^{2}+y^{2}+6 x+10 y+34}+\sqrt{x^{2}+y^{2}+6 x+6 y+18}=2 \\
y^{2}+x^{2}-4 x+10=a
\end{array}\right.
$$
has exactly one solution.
$$
\left\{\begin{array}{c}
\sqrt{x^{2}+y^{2}+6 x+10 y+34}+\sqrt{x^{2}+y^{2}+6 x+6 y+18}=2 \\
y^{2}+x^{2}-4 x+10=a
\end{array}\right.
$$
has exactly one solution.