(1)圆心到两直线的距离相等肆族且为圆半径,L1、L2平行,r =d/2=1圆裂枯弊心在直线y=x与x+y-4=0的交点上,得圆心坐标(2,2)圆方程:(x-2)²+(y-2)²=1(2)设A(s,s+m),B(2s,2s+m)代入圆方程中,得(s-2)²+(s+m-2)²败顷=1..............(1)(2s-2)² +(2s+m-2)² =1 ..............(2)得 s=1 m=1故L直线方程:x-y+1=0