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Консультация № 200486
25.03.2021, 11:31
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Здравствуйте, уважаемые эксперты! Прошу вас ответить на следующий вопрос:На эллипсе
x^2+y^2/25=1 найти точки, из которых отрезок, соединяющий фокусы, виден под углом 60 градусов.
x^2+y^2/25=1 найти точки, из которых отрезок, соединяющий фокусы, виден под углом 60 градусов.
Обсуждение
25.03.2021, 13:42
общий
Адресаты:
Когда какая-то звезда на небе видна "под углом 60 градусов", это выражение означает, что угол 60° измеряется м-ду горизонтом Земли и лучом на звезду.
В Вашем Условии "отрезок, соединяющий фокусы, виден под углом 60 градусов" - я не могу понять, между которыми лучами или горизонталью Вы хотите получить угол 60° ?
В Вашем Условии "отрезок, соединяющий фокусы, виден под углом 60 градусов" - я не могу понять, между которыми лучами или горизонталью Вы хотите получить угол 60° ?
25.03.2021, 14:31
общий
Адресаты:
Ваш эллипс сильно вытянутый по вертикали. Скриншот прилагаю.
Дальше сами справитесь?
Дальше сами справитесь?
26.03.2021, 09:00
общий
это ответ
Здравствуйте, Vlad_ok!
Из уравнения эллипса следует, что эллипс вытянут вдоль оси ординат, его малая полуось
большая полуось 
центр эллипса расположен в начале координат. Поскольку 
постольку 
а фокусы этого эллипса находятся в точках 
Точки эллипса удовлетворяют уравнению 
Пусть точка
принадлежит рассматриваемому эллипсу и из этой точки отрезок 
виден под углом 
Тогда косинус угла между векторами 
и 
удовлетворяет уравнению 
При этом
То есть в искомое множество входят точки
а также, в силу симметрии эллипса относительно оси абсцисс, точки 
Литература
Письменный Д. Т. Конспект лекций по высшей математике: [в 2 ч.]. Ч. 1. -- М.: Айрис-пресс, 2007. -- 288 с.
Из уравнения эллипса следует, что эллипс вытянут вдоль оси ординат, его малая полуось
большая полуось центр эллипса расположен в начале координат. Поскольку постольку а фокусы этого эллипса находятся в точках Точки эллипса удовлетворяют уравнению Пусть точка
принадлежит рассматриваемому эллипсу и из этой точки отрезок виден под углом Тогда косинус угла между векторами и удовлетворяет уравнению При этомТо есть в искомое множество входят точки
а также, в силу симметрии эллипса относительно оси абсцисс, точки Литература
Письменный Д. Т. Конспект лекций по высшей математике: [в 2 ч.]. Ч. 1. -- М.: Айрис-пресс, 2007. -- 288 с.
5
Об авторе:
Facta loquuntur.
Facta loquuntur.
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