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Консультация № 183253
19.05.2011, 21:50
67.97 руб.
0
4
3
Пожалуйста помогите решить 2 нетрудные задачки по "Аналитической Геометрии" :)
1) Составить уровнение геометрического места точек , одинаково удалённых от т. А(0.3) и от оси Ох.
Если можно нарисовать график то пожалуйста нарисуйте :)
2)Уравнение кривой 2ого порядка путём выделение полного квадрата привести к каноническому виду . Построить нужно кривую.
3x^2+12y^2-4x+16y+7=0
Спасибо заранее...
1) Составить уровнение геометрического места точек , одинаково удалённых от т. А(0.3) и от оси Ох.
Если можно нарисовать график то пожалуйста нарисуйте :)
2)Уравнение кривой 2ого порядка путём выделение полного квадрата привести к каноническому виду . Построить нужно кривую.
3x^2+12y^2-4x+16y+7=0
Спасибо заранее...
Обсуждение
19.05.2011, 23:28
общий
это ответ
Здравствуйте, Sasha23!
Рассмотрим вторую задачу. Выполним следующие преобразования:
Полученное уравнение задаёт мнимый эллипс, которому не удовлетворяют координаты ни одной точки.
С уважением.
Рассмотрим вторую задачу. Выполним следующие преобразования:
Полученное уравнение задаёт мнимый эллипс, которому не удовлетворяют координаты ни одной точки.
С уважением.
5
Об авторе:
Facta loquuntur.
Facta loquuntur.
19.05.2011, 23:41
общий
это ответ
Здравствуйте, Sasha23!
Решение задачи 2 в прикрепленном файле.
Решение задачи 2 в прикрепленном файле.
Прикрепленные файлы:
5
20.05.2011, 00:32
общий
это ответ
Здравствуйте, Sasha23!
Задача 1.
r1=r2
r1=[$8730$](x2+(y-3)2) (гипотенуза прямоугольного треугольника)
r2=y
Отсюда
[$8730$](x2 + (y-3)2) = y
x2 + y2- 6y + 9 = y2
x2 + 9 = 6y
y=1/6 x2 + 1.5
Кривая - парабола.
Параболой называется геометрическое место точек, одинаково удаленных от данной точки (фокуса) и данной прямой (директрисы).
Фокус у нас в точке F(0,3), директриса - ось OX, уравнение которой y=0
Задача 1.
r1=r2
r1=[$8730$](x2+(y-3)2) (гипотенуза прямоугольного треугольника)
r2=y
Отсюда
[$8730$](x2 + (y-3)2) = y
x2 + y2- 6y + 9 = y2
x2 + 9 = 6y
y=1/6 x2 + 1.5
Кривая - парабола.
Параболой называется геометрическое место точек, одинаково удаленных от данной точки (фокуса) и данной прямой (директрисы).
Фокус у нас в точке F(0,3), директриса - ось OX, уравнение которой y=0
Прикрепленные файлы:
5
20.05.2011, 02:10
общий
Рассмотрим первую задачу.
Пусть некоторая точка M(x, y) принадлежит искомому геометрическому месту. Квадрат расстояния от этой точки до точки A(0, 3) определяется выражением
а квадрат расстояния от этой точки до оси Ox - выражением
Приравнивая оба выражения, получим
Получили каноническое уравнение параболы, симметричной относительно оси Oy, с вершиной в точке (0, 3/2).
Можно уравнение параболы преобразовать так:
и построить параболу "по точкам".
Пусть некоторая точка M(x, y) принадлежит искомому геометрическому месту. Квадрат расстояния от этой точки до точки A(0, 3) определяется выражением
а квадрат расстояния от этой точки до оси Ox - выражением
Приравнивая оба выражения, получим
Получили каноническое уравнение параболы, симметричной относительно оси Oy, с вершиной в точке (0, 3/2).
Можно уравнение параболы преобразовать так:
и построить параболу "по точкам".
Об авторе:
Facta loquuntur.
Facta loquuntur.
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