CGPET 2011 Solved Paper

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