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Консультация № 144881
24.09.2008, 14:32
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Здравствуйте!Я затрудняюсь в решении этого задания:Найти ур-ние геометрического места точек, каждая из которых находиться в двое больше от т.А(3,0), чем от оси координат.Заранее благодарю всех откликнувшихся!!! 
Обсуждение
25.09.2008, 22:02
общий
это ответ
Здравствуйте, Григорук Илья Игоревич!
Решение.
Пусть имеется точка M(x; y), такая, что расстояние до нее от точки A(3; 0) вдвое больше, чем до оси ОРДИНАТ . Тогда координаты этой точки удовлетворяют равенству
[$8730$]((x - 3)^2 + y^2) = 2x (*).
Выполним следующие преобразования выражения (*):
(x - 3)^2 + y^2 = 4x^2,
x^2 - 6x + 9 + y^2 = 4x^2,
3x^2 + 6x - y^2 - 9 = 0,
3(x^2 + 2x + 1) - y^2 - 9 - 3 = 0,
3(x + 1)^2 - y^2 = 12,
((x + 1)^2)/(2^2) - (y^2)/((2[$8730$]3)^2) = 1 (**).
Уравнение (**) задает гиперболу...
С уважением.
Решение.
Пусть имеется точка M(x; y), такая, что расстояние до нее от точки A(3; 0) вдвое больше, чем до оси ОРДИНАТ . Тогда координаты этой точки удовлетворяют равенству
[$8730$]((x - 3)^2 + y^2) = 2x (*).
Выполним следующие преобразования выражения (*):
(x - 3)^2 + y^2 = 4x^2,
x^2 - 6x + 9 + y^2 = 4x^2,
3x^2 + 6x - y^2 - 9 = 0,
3(x^2 + 2x + 1) - y^2 - 9 - 3 = 0,
3(x + 1)^2 - y^2 = 12,
((x + 1)^2)/(2^2) - (y^2)/((2[$8730$]3)^2) = 1 (**).
Уравнение (**) задает гиперболу...
С уважением.
Об авторе:
Facta loquuntur.
Facta loquuntur.
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