一动圆与已知圆O2:(x-2)²+y²=81内切,与已知圆O1:(x+2)²+y²=1外切,求动圆圆C的轨迹方程.要完整步骤(急!)
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![一动圆与已知圆O2:(x-2)²+y²=81内切,与已知圆O1:(x+2)²+y²=1外切,求动圆圆C的轨迹方程.要完整步骤(急!)](/uploads/image/z/6933637-37-7.jpg?t=%E4%B8%80%E5%8A%A8%E5%9C%86%E4%B8%8E%E5%B7%B2%E7%9F%A5%E5%9C%86O2%3A%28x-2%29%26%23178%3B%2By%26%23178%3B%3D81%E5%86%85%E5%88%87%2C%E4%B8%8E%E5%B7%B2%E7%9F%A5%E5%9C%86O1%3A%28x%2B2%29%26%23178%3B%2By%26%23178%3B%3D1%E5%A4%96%E5%88%87%2C%E6%B1%82%E5%8A%A8%E5%9C%86%E5%9C%86C%E7%9A%84%E8%BD%A8%E8%BF%B9%E6%96%B9%E7%A8%8B.%E8%A6%81%E5%AE%8C%E6%95%B4%E6%AD%A5%E9%AA%A4%28%E6%80%A5%21%29)
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一动圆与已知圆O2:(x-2)²+y²=81内切,与已知圆O1:(x+2)²+y²=1外切,求动圆圆C的轨迹方程.要完整步骤(急!)
一动圆与已知圆O2:(x-2)²+y²=81内切,与已知圆O1:(x+2)²+y²=1外切,
求动圆圆C的轨迹方程.要完整步骤(急!)
一动圆与已知圆O2:(x-2)²+y²=81内切,与已知圆O1:(x+2)²+y²=1外切,求动圆圆C的轨迹方程.要完整步骤(急!)
答:
(x-2)²+y²=81,圆心为(2,0),半径R=9
(x+2)²+y²=1,圆心为(-2,0),半径r=1
设动圆半径为m,动圆圆心为(x,y)
则外切圆圆心距=1+m>1,内切圆圆心距=9-m>0
所以:
√[(x+2)²+y²]=1+m
√[(x-2)²+y²]=9-m
两式相加得:
√[(x+2)²+y²]+√[(x-2)²+y²]=10
就是动点(x,y)到两定点(-2,0)和(2,0)的距离之和为10
2a=10,a=5
2c=F1F2=2-(-2)=4,c=2
所以:b²=a²-c²=21
所以:轨迹为x²/25+y²/21=1