y = mx - b√1+m2 is a tangent to the circle x2+y2=b2 for all values of m. if it also touches thecircle (x−a)2+y2=b2 , then the length of the perpendicular from its centre (a,0) on this line is equalto the radius b of the circle, which gives.
ma−b√1+m2
√1+m2
= ±b Taking negative value on R.H.S we get m=0, so we neglect it. Taking the positive value on R.H.S we get ma = 2b√1+m2 ⇒ m2(a2−4b2) = 4b2 ⇒ m =