x^2+y^2+2mx+my+4=0
x^2+2mx+m^2+y^2+my+m^2/4=-4+5m^2/4
(x+m)^2+(y+m/2)^2=5m^2/4-4
5m^2/4-4≥0
m^2≥16/5
m≥4√5/5或m≤-4√5/5
取等号的时候是点圆.