The centre and radius of the first circle x2+y2+2x+8y−23=0 are C1(−1,−4) and r1=√40 Similarly, the centre and radius of second circle x2+y2−4x−10y+9=0 are C2(2,5) and r2=√20 Now, C1C2=√(2+1)2+(5+4)2 =√9+81=√90 r1+r2=√40+√20 r1−r2=√40−√20 Here, r1−r2<C1C2<r1+r2 ∴ Two common tangents can be drawn.