COMEDK Exam 2022 Solved Paper

Centre and radii of the given circles are C1(1,3) ,
r1=r and C2(4,−1),r2=3 respectively. Since, circles intersect in two distinct points, then
|r1−r2|<C1C2<r1+r2
⇒ |r−3|<5<r+3 ..................(i)
From last two relations, r>2
From first two relations,
|r−3|<5
⇒ −5<r−3<5
⇒ −2<r<8 ..................(ii)
∴ From Eq.(i) and Eq.(ii), we get
2<r<8