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 .