(1)直线代入圆,x²+x²+2bx+b²+2x-2x-2b+2-4=0
2x²+2bx+b²-2b-2=0
∵相切
∴⊿=4b²-8b²+16b+16=-4b²+16b+16=0
∴b=2±2√2
(2)直线代入圆,x²+x²+8x+16+2ax-2ax-8a+2a²-4a=0
2x²+8x+2a²-12a+16=0
x²+4x+(a²-6a+8)=0
⊿=16-4a²+24a-32=-4a²+24a-16≥0
∴3-√5≤a≤3+√5
设交点(x1,y1) (x2,y2)
∴x1+x2=-4 x1x2=a²-6a+8
y1+y2=(x1+x2)+8=4 y1y2=x1x2+4(x1+x2)+16=a²-6a+8
∴弦长=√[(x1-x2)²+(y1-y2)²]=√[(x1+x2)²-4x1x2+(y1+y2)²-4y1y2]=√(16-4a²+24a-32+16-4a²+24a-32)
=√(-8a²+48a-32)=√[-8(x-3)²+40]
∴当x=3时,弦长最大值为√40=2√10