Let S1≡x2+y2+4x−6y−3=0 ⇒g=2,f=−3,C1=−3 [∵r=√g2+f2−c and centre =(−g,−f)] Centre, C1(−2,3) radius, r1=√(−2)2+32+3=4 and S2≡x2+y2+4x−2y+1=0 ⇒g2=2,f2=−1,C2=1
Centre, C2(−2,1) Radius, r2=√(−2)2+12−1=2 Distance between centres C1C2=√02+22=2 Difference in radius |r1−r2|=2 ∵C1C2=|r−r2| ∴ Circle touches each other internally at one point ⇒ Number of tangents =1