ГДЗ по алгебре 9 класс Макарычев Задание 451

\[\boxed{\text{451\ (451).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[\text{M\ }(1;2);\ \ y = kx:\]

\[2 = k \cdot 1\]

\[k = 2\]

\[y = 2x.\]

\[\left\{ \begin{matrix} (x - 4)^{2} + (y - 6)^{2} = 25 \\ y = 2x\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \Longrightarrow\]

\[\Longrightarrow \left\{ \begin{matrix} (x - 4)^{2} + (2x - 6)^{2} = 25 \\ y = 2x\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \]

\[\Longrightarrow \left\{ \begin{matrix} x^{2} - 8x + 16 + 4x^{2} - 24x + 36 = 25 \\ y = 2x\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \]

\[\Longrightarrow \left\{ \begin{matrix} 5x^{2} - 32x + 27 = 0 \\ y = 2x\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \]

\[5x^{2} - 32x + 27 = 0\]

\[D_{1} = 16^{2} - 27 \cdot 5 =\]

\[= 256 - 135 = 121\]

\[x_{1,2} = \frac{16 \pm 11}{5} = 1;5,4.\]

\[\left\{ \begin{matrix} x_{1} = 1 \\ y_{1} = 2 \\ \end{matrix} \right.\ \text{\ \ \ }или\ \ \ \left\{ \begin{matrix} x_{2} = 5,4\ \ \ \\ y_{2} = 10,8. \\ \end{matrix} \right.\ \]

\[Ответ:точка\ (5,4;10,8).\]