EAMCET Engineering 2006 Solved Paper

The equations of circles are x2+y2−8x+2y=0 and
x2+y2−2x−16y+25=0‌. ‌
The centre and radius of first circle are C1(4,−1) and √17 respectively. Also the centre and radius of second circle are C2(1,8) and √40 respectively.
∵‌C1C2‌=√(1−4)2+(8+1)2
‌=√9+81=√90
‌‌ and ‌‌‌r1+r2‌=√17+√40
∵‌C1C2‌<r1+r2
∴ These two circles internally
Thus the number of common tangents is 2 .