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Консультация № 196765
22.10.2019, 18:47
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Здравствуйте, уважаемые эксперты! Прошу вас ответить на следующий вопрос:
Объясните пожалуйста как это решать: Найти геометрическое место точек удаленных от окружности x^2 +y^2=1 в два раза ближе, чем от окружности (x-6)^2 +y^2=4
Объясните пожалуйста как это решать: Найти геометрическое место точек удаленных от окружности x^2 +y^2=1 в два раза ближе, чем от окружности (x-6)^2 +y^2=4
Обсуждение
26.10.2019, 16:36
общий
это ответ
Здравствуйте, nnnnngg!
Наверное, автор задачи имел в виду, что расстояние от точек, принадлежащих искомому геометрическому месту, до окружности
в два раза меньше, чем до окружности 
Тогда, в соответствии с наглядными представлениями (рисунок в прикреплённом файле; заданные окружности обозначены синим и зелёным цветами), в данном случае расстояние от точки 
принадлежащей искомому геометрическому месту, до окружности равно разности расстояния от этой точки до окружности и радиуса окружности. Тогда, согласно условию задачи, получим
Из последнего уравнения видно, что искомое геометрическое место точек представляет собой окружность, центр которой находится в точке
а радиус равен четырём единицам длины [1, с. 63]. На рисунке эта окружность показана красным цветом.
Литература
1. Письменный Д. Т. Конспект лекций по высшей математике. В 2 ч. Ч. 1. -- М.: Айрис-пресс, 2006. -- 288 с.
Наверное, автор задачи имел в виду, что расстояние от точек, принадлежащих искомому геометрическому месту, до окружности
в два раза меньше, чем до окружности Тогда, в соответствии с наглядными представлениями (рисунок в прикреплённом файле; заданные окружности обозначены синим и зелёным цветами), в данном случае расстояние от точки принадлежащей искомому геометрическому месту, до окружности равно разности расстояния от этой точки до окружности и радиуса окружности. Тогда, согласно условию задачи, получимИз последнего уравнения видно, что искомое геометрическое место точек представляет собой окружность, центр которой находится в точке
а радиус равен четырём единицам длины [1, с. 63]. На рисунке эта окружность показана красным цветом.Литература
1. Письменный Д. Т. Конспект лекций по высшей математике. В 2 ч. Ч. 1. -- М.: Айрис-пресс, 2006. -- 288 с.
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Об авторе:
Facta loquuntur.
Facta loquuntur.
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