x∧2+y∧2-4x+2my+2m∧2-2m+1=0(x-2)²+(y+m)²=-m²+2m+3要使它表示一个圆，则有-m&sup
x∧2+y∧2-4x+2my+2m∧2-2m+1=0(x-2)²+(y+m)²=-m²+2m+3要使它表示一个圆，则有-m²+2m+3>0m²-2m-3<0(m-3)(m+1)<0-1<m<3令f(m)=-m²+2m+3=-(m-1)²+4当m=1时，f(m)取最大值4此时圆的半径最大圆的方程是(x-2)²+(y+1)²=2²圆心是(2,-1),半径是2
x^2+y^2-4x+2mx+2m^2-2m+1=0(x^2-(4-2m)x+(2-m)^2)+y^2=-m^2-2m+3[x-(2-m)]^2+y^2=-m^2-2m+3当-m^2-2m+3>0时,表示圆.m^2+2m-3<0(m+3)(m-1)<0即-3<m<1r^2=-m^2-2m+3=-(m+1)^2+4当m=-1时,半径r最大是2
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x∧2+y∧2-4x+2my+2m∧2-2m+1=0
(x-2)²+(y+m)²=-m²+2m+3
要使它表示一个圆，则有
-m²+2m+3>0
m²-2m-3<0
(m-3)(m+1)<0
-1<m<3
令f(m)=-m²+2m+3=-(m-1)²+4
当m=1时，f(m)取最大值4
此时圆的半径最大
圆的方程是(x-2)²+(y+1)²=2²
圆心是(2,-1),半径是2
x^2+y^2-4x+2mx+2m^2-2m+1=0
(x^2-(4-2m)x+(2-m)^2)+y^2=-m^2-2m+3
[x-(2-m)]^2+y^2=-m^2-2m+3
当-m^2-2m+3>0时,表示圆.
m^2+2m-3<0
(m+3)(m-1)<0
即-3<m<1
r^2=-m^2-2m+3=-(m+1)^2+4
当m=-1时,半径r最大是2