\[\boxed{\text{409\ (409).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
Пояснение.
Решение.
\[(x - 5)^{2} + (y - 7)^{2} = r^{2}\]
\[\textbf{а)}\ точка\ касания\ (5;0):\ \ \ \]
\[(5 - 5)^{2} + (0 - 7)^{2} = 49;\]
\[\Longrightarrow r^{2} = 49 \Longrightarrow r = 7.\]
\[\textbf{б)}\ точка\ касания\ (0;7):\ \ \ \]
\[(0 - 5)^{2} + (7 - 7)^{2} = 25;\]
\[\Longrightarrow r^{2} = 25 \Longrightarrow r = 5.\]
\[\boxed{\text{409.}\text{\ }\text{ОК\ ГДЗ\ -\ домашка\ на\ 5}}\]
\[\left\{ \begin{matrix} x + y = a + 1\ \ \\ 3x - y = a - 1 \\ \end{matrix} \right.\ \]
\[\left\{ \begin{matrix} y = a + 1 - x\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ 3x - (a + 1 - x) = a - 1 \\ \end{matrix} \right.\ \Longrightarrow\]
\[\Longrightarrow \left\{ \begin{matrix} y = a + 1 - x \\ 4x = 2a\ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \Longrightarrow\]
\[\Longrightarrow \left\{ \begin{matrix} y = a + 1 - 0,5a \\ x = 0,5a\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \Longrightarrow\]
\[\Longrightarrow \left\{ \begin{matrix} y = 0,5a + 1 \\ x = 0,5a\ \ \ \ \ \ \ \\ \end{matrix} \right.\ \]
\[так\ как\ x > 0\ \ и\ \ y > 0 \Longrightarrow a > 0.\]
\[Ответ:при\ a > 0.\]