若圆(x-a)^2+(y-b)^2=6始终平分圆x^2+y^2+2x+2y-3=0的周长,则动点M(a,b)的轨迹方程是?

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若圆(x-a)^2+(y-b)^2=6始终平分圆x^2+y^2+2x+2y-3=0的周长,则动点M(a,b)的轨迹方程是?

若圆(x-a)^2+(y-b)^2=6始终平分圆x^2+y^2+2x+2y-3=0的周长,则动点M(a,b)的轨迹方程是?
若圆(x-a)^2+(y-b)^2=6始终平分圆x^2+y^2+2x+2y-3=0的周长,则动点M(a,b)的轨迹方程是?

若圆(x-a)^2+(y-b)^2=6始终平分圆x^2+y^2+2x+2y-3=0的周长,则动点M(a,b)的轨迹方程是?
x²+y²-2ax-2by+a²+b²-6=0
x²+y²+2x+2y-3=0
相减
(2+2a)x+(2+2b)y+3-a²-b²=0
这就是两圆交点所在直线
始终平分则该直线过第二个园的圆心
圆心是(-1,-1)
所以-(2+2a)-(2+2b)+3-a²-b²=0
M即x=a,y=b
所以x²+y²+2x+2y+1=0

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