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Консультация № 109117
12.11.2007, 20:19
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Парабола, симметричная относительно оси ОУ проходит через точки пересечения линий у=-х и х в квадрате + у в квадрате + 6у в квадрате =0.
Надо записать ур-е параболы.
Помогите пожалуйста очень нужно! Заранее благодарю!!!!!!!!
Надо записать ур-е параболы.
Помогите пожалуйста очень нужно! Заранее благодарю!!!!!!!!
Обсуждение
Неизвестный
16.11.2007, 05:56
общий
это ответ
Здравствуйте, Caspersurgut!
Скорее всего, у вас опечатка? Парабола, симметричная относительно оси ОУ, проходит через точки пересечения линий у=-х и х² + у² + 6у = 0?
Если так, то последнее уравнение - это уравнение окружности х² + у² + 6у + 9 - 9 = х² + (у + 3)² - 9 = 0 с центром в (0; -3) и радиусом 3.
Точки пересечения этой окружности и прямой (0; 0) и (3; -3)
Так как требуемая парабола симметрична относительно оси y, то она проходит и через точку (-3; -3)
Отсюда ясно, что эта парабола с вершиной в (0, 0), с ветвями, опущенными вниз, и проходящая через точки (3; -3) и (-3; -3)
y = -ax²
-3 = -a3² => a = 1/3
Ответ: y = -x²/3
Скорее всего, у вас опечатка? Парабола, симметричная относительно оси ОУ, проходит через точки пересечения линий у=-х и х² + у² + 6у = 0?
Если так, то последнее уравнение - это уравнение окружности х² + у² + 6у + 9 - 9 = х² + (у + 3)² - 9 = 0 с центром в (0; -3) и радиусом 3.
Точки пересечения этой окружности и прямой (0; 0) и (3; -3)
Так как требуемая парабола симметрична относительно оси y, то она проходит и через точку (-3; -3)
Отсюда ясно, что эта парабола с вершиной в (0, 0), с ветвями, опущенными вниз, и проходящая через точки (3; -3) и (-3; -3)
y = -ax²
-3 = -a3² => a = 1/3
Ответ: y = -x²/3
Форма ответа
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