\[x^{2} + y^{2} - 2x = 8y - 17\]
\[x^{2} - 2x + 1 + y^{2} - 8y + 16 = 0\]
\[(x - 1)^{2} + (y - 4)^{2} = 0\]
\[x = 1;\ \ \ \ \ \ \ \ \ y = 4.\]
\[Ответ:(1;4)\text{.\ }\]