Given circles are x2+y2−4x−6y−3=0 . . . (i) and ‌‌x2+y2+2x+2y+1=0 . . . (ii) For circle (i), g1=−2,f1=−3,c1=−3 ∴ Centre C1(2,3) and r1=√4+9+3=4 and for circle (ii), g2=1,f2=1,c2=1 ∴ Centre C2(−1,−1) and r2=√1+1−1=1 Now, ‌‌C1C2=√(2+1)2+(3+1)2=√9+16=5 and ‌‌r1+r2=4+1=5 So, ‌‌C1C2=r1+r2 Thus, both the circles touch each other externally. Hence, number of common tangents =3