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Задать вопрос экспертам

Консультация № 195349

22.04.2019, 06:21

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Образование

Здравствуйте! У меня возникли сложности с таким вопросом:

Прикрепленные файлы:

1dfe9f2781a1197461eae08dd4ea10721f6b1213.docx

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Обсуждение

давно

Лангваген Сергей Евгеньевич

Советник
165461
578

22.04.2019, 13:30

общий

это ответ

Здравствуйте, yelena_trushina!

Составляем уравнение линии, каждая точка которой равноудалена
от точки (2, -6) и прямой x+2 = 0.

Расстояние от произвольной точки (x,y) плоскости до точки (2, -6) равно
d₁ = [$8730$]((x-2)² + (y+6)²),
расстояние до прямой равно
d₂ = |x + 2|.
На линии, уравнение которой требуется найти,
d₁ = d₂,
то есть
|x+2| = [$8730$]((x-2)² + (y + 6)²).
Возводя обе части в квадрат, получим
(x+2)² = (x-2)² + (y + 6)², x² + 4x +4 = x² - 4x + 4 + (y+6)²,
и окончательно
8x = (y + 6)² -- уравнение параболы с вершиной в точке (0, -6),
ветви которой направлены вдоль оси x.

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