Ответ:

[tex]y = - \frac{ 1 }{ 3 } x+ \frac{ 2 }{ 3 }[/tex]

Пошаговое объяснение:

[tex]{\sqrt{(x - x_M)^2 + (y - y_M)^2} = \sqrt{(x - x_N)^2 + (y - y_N)^2}}\ \ \ \ \ |()^2\\\\ (x - x_M)^2 + (y - y_M)^2 = (x - x_N)^2 + (y - y_N)^2\\\\ (x - 6)^2 + (y - 2)^2 = (x - 4)^2 + (y + 4)^2\\\\ x^2 - 12x + 36 + y^2 - 4y + 4 = x^2 - 8x + 16 + y^2 + 8y + 16\\\\ - 4 y - 8y = x^2 - 8x + 16 + y^2 + 16 - x^2 + 12x - 36 - y^2 - 4\\\\ - 12y = 4x - 8\ \ \ |:\left( -12\right) \\\\ \underline{y = - \frac{ 1 }{ 3 } x+ \frac{ 2 }{ 3 }}[/tex]