Substitute into the cyclic equation:

x？ +(-x+b)？ +4x-4=0, get

2x？ +(4-2b)x+b？ -4=0

The straight line is tangent to the circle, and the equation discriminant =0.

(4-2b)？ -8(b？ -4)=0

b？ +4b- 12=0

(b+6)(b-2)=0

B=-6 or b=2.

The linear equation is y=-x-6 or y=-x+2.