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Консультация № 184490

18.11.2011, 11:52

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Образование

Здравствуйте! У меня возникли сложности с таким вопросом:
Написать уравнение кривой, сумма квадратов расстояний от каждой точки которой до точек A(-3,0).B(0,3) и C(3,0) равна 27.

Обсуждение

давно

Орловский Дмитрий

Мастер-Эксперт
319965
1463

18.11.2011, 12:21

общий

это ответ

Здравствуйте, владимир!
Пусть M(x,y) произвольная точка кривой.
Квадрат расстояния от M до A равен (x+3)²+y²
Квадрат расстояния от M до B равен x²+(y-3)²
Квадрат расстояния от M до C равен (x-3)²+y²
Уравнение кривой:
(x+3)²+y²+x²+(y-3)²+(x-3)²+y²=27
x²+6x+9+y²+x²+y-6y+9+x²-6x+9+y²=27
3x²+3y²-6y=0
x²+y²-2y=0
x²+(y-1)²-1=0
x²+(y-1)²=1

Окружность с центром (0;1) радиуса 1.

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