圆M:x²+y²-2mx-2ny+m²-1=0与圆N:x²+y²+2x+2y-2=0交于A,B两点,且这两点平分圆N

问题描述:

圆M:x²+y²-2mx-2ny+m²-1=0与圆N:x²+y²+2x+2y-2=0交于A,B两点,且这两点平分圆N
求圆M的圆心的轨迹方程,并求其中半径最小时的圆M的方程.

AB两点两点平分圆N圆 AB为N圆直径 圆M; (x-m)^2+(y-n)^2=1+n^2,圆心M(m,n) 圆N:(x+1)^2+(y+1)^2=4,圆心N(-1,-1) AB=2R=4 R^2+MN^2=AM^2 4+(m+1)^2+(n+1)^2=n^2+1 M圆心轨迹:x^2+2x+2y+5=0 2)x^2+2x+2y+5=0 (x+1...