Circle I : x2+y2−6x−4y+9=0 Circle II : x2+y2+2x+2y−7=0 Point of contact : (α,β) ⇒(x−3)2+(y−2)2=4 Center =(3,2) (x+1)2+(y+1)2=9 centre (−1,−1) Slope of line (m)=‌
3
4
Equation of line y−2=‌
3
4
(x−3) ⇒3x−4y−1=0 The point of contact ( α,β ) lies on the line 3x−4y−1=0 ⇒ Radii are r1=2 and r2=3 Ratio =2:3 Using section formula ‌α=‌