Let c1 and c2 are the centres and r1 and r2 are the radius of the two circles. ∴c1=(3,4),c2=(−1,1)⇒rt=4,r2=1 c1c2=√42+32=5 and r1+r2=5. ⇒c1c2=r1+r2 ∴ Circles touch each other externally. ∴ Transverse common tangent is (x2+y2−6x−8y+9)−(x2+y2+2x−2y+1)=0 ⇒−8x−6y+8=0⇒4x+3y−4=0