12. For what value of $a$ does $\left\{\begin{array}{l}x^{2}+y^{2}+2 x \leqslant 1 \\ x-y+a=0\end{array}\right.$ have a unique solution?
12. From the known simplification, we get $2 x^{2}+(2 a+2) x+a^{2}-1 \leqslant 0$, then $\Delta=0$, which gives $a=-1$ or $a=3$.