P(2,-3)不在C1上×
C1:
(x-4)^2-16+(y-2)^2-4+11=0
(x-4)^2+(y-2)^2=3^2
C2:
(x+2)^2+(y+1)^2=2^2
yu圆心距|C1C2|=√（36+9）=3√5
|PQ|min=|C1C2|-R-r=3√5-3-2=√5(3-√5)