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Здравствуйте! У меня возникли сложности с таким вопросом: составить уравнение линии, каждая точка которой находится втрое дальше от точки А(3;0), чем от точки В(0;2).
Здравствуйте, Посетитель - 395803! Расстояние от точки M(x,y) до точки A(3;0) равно ((x-3)2+y2)1/2 Расстояние от точки M(x,y) до точки B(0;2) равно (x2+(y-2)2)1/2 По условию ((x-3)2+y2)1/2=3(x2+(y-2)2)1/2 Возводя в квадрат и упрощая, получаем x2-6x+9+y2=9(x2+y2-4y+4) 8x2+8y2+6x-36y+27=0 Выделяя полные квадраты, получаем 8(x+3/8)2+8(y-9/4)2=117/8 (x+3/8)2+(y-9/4)2=117/64 Это окружность с центром в точке (-3/8;9/4) радиуса R=[$8730$](117)/8
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принадлежит искомой линии. Тогда
или 
откуда получаем
Радиус окружности равен 
Гордиенко Андрей Владимирович 