Вопрос школьника по предмету Математика
Составить уравнение гиперболы, если 2а = 10 и 2b = 8.
Ответ учителя по предмету Математика
Ответ:
Искомое уравнение гиперболы: (х²/36) — (у²/64) = 1.
Пошаговое объяснение:
Так как уравнения асимптот у = +- (4/3)х, то в = 4к, а = 3к.
По заданию с = 20/2 = 10.
Тогда по уравнению с² = а² + в² получим:
100 = 16к² + 9к² = 25к².
Отсюда к = √(100/25) =√4 = 2.
Получаем значения а = 3*2 = 6, в = 4*2 = 8.
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