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Консультация № 194213
17.12.2018, 18:30
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Здравствуйте! У меня возникли сложности с таким вопросом:
. привести к каноническому виду уравнение кривой 4x^2+4xу+у^2+8x+4у-41=0
. привести к каноническому виду уравнение кривой 4x^2+4xу+у^2+8x+4у-41=0
Обсуждение
20.12.2018, 18:27
общий
это ответ
Здравствуйте, lenocvol!
Сравнивая заданное уравнение с общим уравнением кривой второго порядка
установим, что
Имеем
Примем
Тогда 
Повернём декартову прямоугольную систему координат на угол
тогда
и из заданного уравнения кривой получим
После параллельного переноса системы координат
получим каноническое уравнение пары параллельных прямых
Литература. Геометрия и алгебра. Практикум: учебное пособие / Г. П. Размыслович, А. В. Филипцов, В. М. Ширяев. -- Минск: Вышэйшая школа, 2018. -- 382 с.
Сравнивая заданное уравнение с общим уравнением кривой второго порядка
установим, что
Имеем
Примем
Тогда Повернём декартову прямоугольную систему координат на угол
тогдаи из заданного уравнения кривой получим
После параллельного переноса системы координат
получим каноническое уравнение пары параллельных прямых
Литература. Геометрия и алгебра. Практикум: учебное пособие / Г. П. Размыслович, А. В. Филипцов, В. М. Ширяев. -- Минск: Вышэйшая школа, 2018. -- 382 с.
Об авторе:
Facta loquuntur.
Facta loquuntur.
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