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Консультация № 117609
09.01.2008, 12:59
0.00 руб.
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Добрый день! Помогите решить (необходимо действие решения):
1. Найти растояние от точки В (1,0,1) до прямой, заданной системой уравнений
х+2y-z=3
x-z=1
2. При всех значениях параметра А выяснить характер кривой, заданной уровнением
4x(кв)+4xy-y(кв)+1-А=0
зарание благодарен!
1. Найти растояние от точки В (1,0,1) до прямой, заданной системой уравнений
х+2y-z=3
x-z=1
2. При всех значениях параметра А выяснить характер кривой, заданной уровнением
4x(кв)+4xy-y(кв)+1-А=0
зарание благодарен!
Обсуждение
Неизвестный
10.01.2008, 15:54
общий
это ответ
Здравствуйте, Андрей Д!
2.
4x² + 4xy - y² + (1-A) = 0. (*)
Кривая второго порядка имеет общее уравнение вида
Ax² + 2Bxy + Cy² + 2Dx + 2Ey + F = 0.
Значит, в нашем случае
A = 4, B = 2, C = -1, D = 0, E = 0, F = 1 - A.
Вычислим дискриминанты данного уравнения:
δ =
|A B|
|B C|
=
|4 2|
|2 -1|
= -8.
δ < 0, значит, уравнение (*) определяет либо гиперболу, либо пару пересекающихся прямых (в зависимости от Δ).
Δ =
|A B D|
|B C E|
|D E F|
=
|4 2 0|
|2 -1 0|
|0 0 1-A|
= 8A - 8.
Δ = 0 ⇒ A = 1, уравнение (*) определяет пару пересекающихся прямых;
Δ ≠ 0 ⇒ A ≠ 1, уравнение (*) определяет гиперболу.
Ответ: при A = 1 уравнение определяет пару пересекающихся прямых, при A ≠ 1 — гиперболу.
2.
4x² + 4xy - y² + (1-A) = 0. (*)
Кривая второго порядка имеет общее уравнение вида
Ax² + 2Bxy + Cy² + 2Dx + 2Ey + F = 0.
Значит, в нашем случае
A = 4, B = 2, C = -1, D = 0, E = 0, F = 1 - A.
Вычислим дискриминанты данного уравнения:
δ =
|A B|
|B C|
=
|4 2|
|2 -1|
= -8.
δ < 0, значит, уравнение (*) определяет либо гиперболу, либо пару пересекающихся прямых (в зависимости от Δ).
Δ =
|A B D|
|B C E|
|D E F|
=
|4 2 0|
|2 -1 0|
|0 0 1-A|
= 8A - 8.
Δ = 0 ⇒ A = 1, уравнение (*) определяет пару пересекающихся прямых;
Δ ≠ 0 ⇒ A ≠ 1, уравнение (*) определяет гиперболу.
Ответ: при A = 1 уравнение определяет пару пересекающихся прямых, при A ≠ 1 — гиперболу.
Форма ответа
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