Решите уравнение x^2+y^2-2x+6y+10=0.

\[x^{2} + y^{2} - 2x + 6y + 10 = 0\]

\[\left( x^{2} - 2x + 1 \right) + \left( y^{2} + 6y + 9 \right) = 0\]

\[(x - 1)^{2} + (y + 3)^{2} = 0\]

\[\left\{ \begin{matrix} x - 1 = 0 \\ y + 3 = 0 \\ \end{matrix} \right.\ \Longrightarrow \left\{ \begin{matrix} x = 1\ \ \ \\ y = - 3 \\ \end{matrix} \right.\ \]

\[Ответ:(1;\ - 3).\]