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Задать вопрос экспертам

Консультация № 180062

27.09.2010, 22:16

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0 1 1

Образование

Составить уравнение линии, сумма расстояния точек которой от точек А(2;4) и В(-4;4) равна 8

Обсуждение

давно

Орловский Дмитрий

Мастер-Эксперт
319965
1463

27.09.2010, 23:14

общий

это ответ

Здравствуйте, Посетитель - 337989.
((x-2)²+(y-4)²)^1/2+((x+4)²+(y-4)²)^1/2=8
((x-2)²+(y-4)²)^1/2=8-((x+4)²+(y-4)²)^1/2
Возводим в квадрат и и приводим подобные члены:
76+12x=16((x+4)²+(y-4)²)^1/2
19+3x=4((x+4)²+(y-4)²)^1/2
Еще раз возводим в квадрат и приводим подобные члены:
7x²+14x+16y²-12y+151=0
7(x+1)²+16(y-4)²=112
(x+1)²/16+(y-4)²/7=1
Получили эллипс с центром (-1;4) и полуосями a=4,b=[$8730$]7

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