动圆M与圆C1x^2+y^2+2x-4y+1=0外切,并且和定圆C2x^2+y^2-10x-4y-71=0内切.求动圆圆心的轨迹方程提供:C1(x+1)^2+(y-2)^2=4C2(x-5)^2+(y-2)^2=100
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![动圆M与圆C1x^2+y^2+2x-4y+1=0外切,并且和定圆C2x^2+y^2-10x-4y-71=0内切.求动圆圆心的轨迹方程提供:C1(x+1)^2+(y-2)^2=4C2(x-5)^2+(y-2)^2=100](/uploads/image/z/10885337-17-7.jpg?t=%E5%8A%A8%E5%9C%86M%E4%B8%8E%E5%9C%86C1x%5E2%2By%5E2%2B2x-4y%2B1%3D0%E5%A4%96%E5%88%87%2C%E5%B9%B6%E4%B8%94%E5%92%8C%E5%AE%9A%E5%9C%86C2x%5E2%2By%5E2-10x-4y-71%3D0%E5%86%85%E5%88%87.%E6%B1%82%E5%8A%A8%E5%9C%86%E5%9C%86%E5%BF%83%E7%9A%84%E8%BD%A8%E8%BF%B9%E6%96%B9%E7%A8%8B%E6%8F%90%E4%BE%9B%EF%BC%9AC1%EF%BC%88x%2B1%29%5E2%2B%28y-2%29%5E2%3D4C2%28x-5%29%5E2%2B%EF%BC%88y-2%29%5E2%3D100)
动圆M与圆C1x^2+y^2+2x-4y+1=0外切,并且和定圆C2x^2+y^2-10x-4y-71=0内切.求动圆圆心的轨迹方程提供:C1(x+1)^2+(y-2)^2=4C2(x-5)^2+(y-2)^2=100
动圆M与圆C1x^2+y^2+2x-4y+1=0外切,并且和定圆C2x^2+y^2-10x-4y-71=0内切.求动圆圆心的轨迹方程
提供:C1(x+1)^2+(y-2)^2=4
C2(x-5)^2+(y-2)^2=100
动圆M与圆C1x^2+y^2+2x-4y+1=0外切,并且和定圆C2x^2+y^2-10x-4y-71=0内切.求动圆圆心的轨迹方程提供:C1(x+1)^2+(y-2)^2=4C2(x-5)^2+(y-2)^2=100
设动圆半径为R
则2+R=MC1
10-R=MC2
所以MC1+MC2=12
M的轨迹是乙C1,C2为焦点的椭圆
C1C2中点(2,2)为椭圆中心
(x-2)^2/a^2+(y-2)^2/b^2=1
a=6
c=3
(x-2)^2/36+(y-2)^2/27=1