Given, C1:x2+y2+2x+4y−20=0 Centre O1(−1,−2),r1=√1+4+20=5 C2:x2+y2+6x−8y+9=0 ⇒(x+3)2+(y−4)2=42 Centre O2:(−3,4);r2=√9+16−9=4 r1+r2=9 and |r1−r2
‌
‌
|=1 Two tangents are there, so n=2
P divides O1 and O2 in 5:4 ratio externally P(‌
(−3×5)−(−1×4)
5−4
,‌
(4×5)−(4×−2)
5−4
) ≡P(−11,28) L is the length of tangent from P to C2 l‌=√(−11+3)2+(28−4)2−42 ‌=√64+576−16 ‌=√624=4√39 ‌