已知动圆C和定圆C1:X^2+(Y-4)^2=64内切和定圆C2:X^2+(Y+4)^2=4外切,设C(X,Y),则25X^2+9Y^2=?????

定圆C1:x^2+(y-4)^2=64,圆心C1(4,0),半径=8,
C2:x^2+(y+4)^2=4,圆心C2(-4,0),半径=2,
设动圆半径=R,圆心C(x,y),
|CC1|=√[(x-4)^2+y^2]=8-R,......(1)(两圆内切,圆心距等于半径之差)
|CC2|=√[(x+4)^2+y^2]=2+R,......(2),(两圆外切,圆心距等于半径之和)
(1)式+(2)式得:
√[(x-4)^2+y^2]+√[(x+4)^2+y^2]=10,
经整理得:
9x^2+25y^2=225,
x^2/25+y^2/9=1,
∴动圆圆心轨迹是一个椭圆.