\[\boxed{\mathbf{961.ОК\ ГДЗ - домашка\ на}\ 5}\]
\[\mathbf{Дан}о:\]
\[A( - 2;4);B( - 5; - 3);C( - 7; - 2);\]
\[D(1;5);\]
\[(x + 5)^{2} + (y - 1)^{2} = 16 \Longrightarrow\]
\[\Longrightarrow O( - 5;1);\ R = 4.\]
\[1)\ A( - 2;4):\]
\[( - 2 + 5)^{2} + (4 - 1)^{2} \neq 16;\]
\[9 + 9 \neq 16;\]
\[18 \neq 16 \Longrightarrow \ A( - 2;4) - вне\ \]
\[круга.\]
\[2)\ B( - 5; - 3):\]
\[( - 5 + 5)^{2} + ( - 3 - 1)^{2} = 16;\]
\[16 = 16 \Longrightarrow B( - 5; - 3) - на\ \]
\[окружности.\]
\[3)\ C( - 7; - 2):\]
\[( - 7 + 5)^{2} + ( - 2 - 1)^{2} \neq 16;\ \]
\[4 + 9 \neq 16;\]
\[13 \neq 16 \Longrightarrow C( - 7; - 2) - внутри\ \]
\[круга.\]
\[4)\ D(1;5):\]
\[(1 + 5)^{2} + (5 - 1)^{2} \neq 16;\]
\[36 + 16 \neq 16\]
\[52 \neq 16 \Longrightarrow \ D(1;5) - вне\ круга.\]
\[Ответ:а)\ C;б)\ B;в)\ A\ и\ \text{D.}\]