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数学
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求与x轴相切,圆心C在直线3x-y=0上,且截直线x-y=0得的弦长为
2
7
的圆的方程.
人气:437 ℃ 时间:2020-01-28 09:06:00
解答
设圆心(t,3t),则由圆与x轴相切,可得半径r=3|t|.
∵圆心到直线的距离d=
|t−3t|
2
=
2
t,
∴由r
2
=d
2
+(
7
)
2
,解得t=±1.
∴圆心为(1,3)或(-1,-3),半径等于3.
∴圆C的方程为 (x+1)
2
+(y+3)
2
=9 或 (x-1)
2
+(y-3)
2
=9.
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