已知圆M：x²+(y-2)²=1,Q是x轴上的动点,QA,QB分别切圆M于A,B两点,

(1)M(0,2),r=1
|AB|=4√2/3
设AB与MQ交于点P
|MP|=√[r^2-(AB/2)^2]=√[1-(4√2/3/2)^2]=1/3
Rt△MAP∽Rt△MQA
AM/MQ=MP/AM
1/MQ=(1/3)/1
MQ=3
Q(a,0)
OQ^2+OM^2=MQ^2
a^2+4=9
a^2=5
a=±√5
k(MQ)=±2/√5
直线MQ的方程有两条:
±2x-√5y+2√5=0
(2)设Q(a,0)
圆Q：(x-a)^2+y^2=QA^2＝QM^2-r^2=a^2+2^2-1=3+a^2.(1)
x^2+(y-2)^2=1.(2)
(1)-(2):
AB:y=0.5ax+1.5
直线AB恒过点(0,1.5).