The chord y−mx−1=0 is tangent to the circle. S1≡x2+y2−4x+1=0 Or, (x−2)2+(y−0)2=3 Thus,
|2m+1|
√1+m2
=√3 4m2+1+4m=3+3m2 (m+2)2=6 m=−2±√6 The equation of chord is, L=y+(2±√6)x−1=0 Let possible point is (x1,y1) for which chord L=0 is chord of contact of the circle. So, xx1+yy1−1=0 And, y+(2±√6)x−1=0 Represent the same line. Therefore,