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Консультация № 190792
27.03.2017, 12:34
0.00 руб.
28.03.2017, 18:47
0
1
1
Здравствуйте эксперты. Прошу Вас помочь в решении задачи по математике.
Заранее большое спасибо!
Написать уравнение касательной к параболе
параллельной прямой, проходящей через точки 
и 
Сделать чертёж.
Заранее большое спасибо!
Написать уравнение касательной к параболе
параллельной прямой, проходящей через точки и Сделать чертёж.Обсуждение
29.03.2017, 09:57
общий
это ответ
Здравствуйте, ms.nastasya2512!
Вычислим угловой коэффициент заданной прямой:
Касательная к параболе тоже должна иметь этот угловой коэффициент, потому что она параллельна заданной прямой. Этот угловой коэффициент равен значению производной функции, графиком которой является заданная парабола, в точке касания
То есть, поскольку
постольку
откуда
Точка
является общей точкой заданной параболы и касательной, уравнение которой нужно вывести. Выведем это уравнение:
или
Последнее выражение является уравнением касательной (в форме уравнения с угловым коэффициентом).
Рисунок к решению задачи показан ниже.
Вычислим угловой коэффициент заданной прямой:
Касательная к параболе тоже должна иметь этот угловой коэффициент, потому что она параллельна заданной прямой. Этот угловой коэффициент равен значению производной функции, графиком которой является заданная парабола, в точке касания
То есть, посколькупостольку
откуда
Точка
является общей точкой заданной параболы и касательной, уравнение которой нужно вывести. Выведем это уравнение:или
Последнее выражение является уравнением касательной (в форме уравнения с угловым коэффициентом).
Рисунок к решению задачи показан ниже.
Об авторе:
Facta loquuntur.
Facta loquuntur.
Форма ответа
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