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shirokoffmitia
@shirokoffmitia
August 2022
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Найти центр и радиус окружности заданной уравнением:
9x²+9y²+6x-24y-28=0
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sangers1959
Verified answer
9x²+9y²+6x-24y-28=0
(3x)²+6x+1+(3y)²-24y+16-1-16-28=0
(3x)²+2*3x*1+1²+(3y)²+2*3y*4+4²-45=0
(3x+1)²+(3y-4)²=(√45)²=(3√5)²
3x+1=0 3x=-1 |÷3 x=-1/3.
3y-4=0 3y=4 |÷3 y-4/3.
Центр заданной окружности (-1/3;4/3), радиус 3√5.
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Verified answer
9x²+9y²+6x-24y-28=0(3x)²+6x+1+(3y)²-24y+16-1-16-28=0
(3x)²+2*3x*1+1²+(3y)²+2*3y*4+4²-45=0
(3x+1)²+(3y-4)²=(√45)²=(3√5)²
3x+1=0 3x=-1 |÷3 x=-1/3.
3y-4=0 3y=4 |÷3 y-4/3.
Центр заданной окружности (-1/3;4/3), радиус 3√5.