The coordinates of the center of a circle, whose radius is 2 unit and which touches the line pair x2−y2−2x+1=0, are

Line pair is (x−1)2−y2=0, i.e., x+y−1=0 and x−y−1=0. Let the center be (α, 0). Then its distance from x + y - 1 = 0 isα−12=2 (radius)   i.e. α=1±22  So, the center may be (1+22,0),(1−22,0).   Now, let the center be (1,β). Then,  1+β−12=2  or  β=±22  So, the center may be (1,22),(1,−22).