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Консультация № 123785
18.02.2008, 23:51
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Здраствуйте. Помогите плиз.
привести уравнение кривой 9x^2+4y^2+18x-8y+49=0 к каноническому виду и построить её график
привести уравнение кривой 9x^2+4y^2+18x-8y+49=0 к каноническому виду и построить её график
Обсуждение
Неизвестный
19.02.2008, 10:06
общий
это ответ
Здравствуйте, Макаров Вячеслав Валерьевич!
9x^2+4y^2+18x-8y+49=0
(9x^2+18x+9)-9 + (4y^2-8y+4)-4+49=0
вынесем за скобки множители
9*(x^2+2x+1)+4*(y^2-2y+1)+36=0
свернём
9*(x+1)^2+4*(y-1)^2=-36
Разделим правую и левую часть на 36
(x+1)^2/4 + (y-1)^2/9 = -1
Это каноническое уравнение элипса с центром в т. (-1;1)
большая полуось которого равна 2, а малая 3.
построить график теперь большого труда не составит.
9x^2+4y^2+18x-8y+49=0
(9x^2+18x+9)-9 + (4y^2-8y+4)-4+49=0
вынесем за скобки множители
9*(x^2+2x+1)+4*(y^2-2y+1)+36=0
свернём
9*(x+1)^2+4*(y-1)^2=-36
Разделим правую и левую часть на 36
(x+1)^2/4 + (y-1)^2/9 = -1
Это каноническое уравнение элипса с центром в т. (-1;1)
большая полуось которого равна 2, а малая 3.
построить график теперь большого труда не составит.
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