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Консультация № 191199
30.06.2017, 04:32
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Уважаемые эксперты! Пожалуйста, ответьте на вопрос:10. Составить уравнение линии, каждая точка которой равноудалена от точки А(3;1) и от прямой Y+5=0.
Обсуждение
30.06.2017, 09:03
общий
это ответ
Здравствуйте, asdf1234!
Пусть точка, принадлежащая линии, уравнение которой нужно составить, имеет координаты
Тогда расстояние от этой точки до точки 
суть 
а расстояние от этой точки до прямой 
или 
суть 
Согласно условию задачи, эти расстояния равны между собой. Тогда
Получили уравнение параболы в каноническом виде. Согласно этому уравнению, ось параболы параллельна оси ординат, ветви направлены вверх, вершиной параболы является точка
расстояние между фокусом и директрисой 
Точка - фокус параболы, прямая 
- директриса параболы.
Пусть точка, принадлежащая линии, уравнение которой нужно составить, имеет координаты
Тогда расстояние от этой точки до точки суть а расстояние от этой точки до прямой или суть Согласно условию задачи, эти расстояния равны между собой. Тогдаsqrt{(x-3)^2+(y-1)^2}=y+5,
Получили уравнение параболы в каноническом виде. Согласно этому уравнению, ось параболы параллельна оси ординат, ветви направлены вверх, вершиной параболы является точка
расстояние между фокусом и директрисой Точка - фокус параболы, прямая - директриса параболы.
Об авторе:
Facta loquuntur.
Facta loquuntur.
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