In List-I, a pair of circles is given in A, B, C and in List-II, angle between those pair of circles is given. Match the items from List-I to List-II. array lll & 1 c List-I & List-II A (x-2)^2+y^2=2(x-2)^2+(y-1)^2=1 & I & 90^ B x^2+y^2-6 x-6 y+9=0 & II 135^ x^2+y^2-4 x+4 y-9=0 & & C x^2+y^2+4 x-14 y+28=0 & III 60^ x^2+y^2+4 x-5=0 & & & & IV 30^ array The correct matching is A B C

Step-by-step solution

We know that, angle between two circles is given by = r₁^2+r₂^2-d^2 2 r₁ r₂ , where r₁ and r₂ are radius and d is distance between centres. (A) aligned & = ( 2 )^2+(1)^2- [ (2-2)^2+(1-0)^2 ]^2 2 2 1 & [ r₁= 2 , r₂=1, c₁=(2,0), c₂=(2,1) ] & = 2+1-1 2 2 = 1 2 aligned =45^ or 135^ (B) aligned = & (3)^2+( 17 )^2- [ (3-2)^2+(3+2)^2 ]^2 2 3 17 & [ r₁=3, r₂= 17 , c₁=(3,3), c₂=(2,-2) ] & = 9+17-26 6 17 =0 & =90^ aligned (C) aligned & = (5)^2+(3)^2- [ (-2+2)^2+(7-0)^2 ]^2 2 5 3 & [ r₁=5, r₂=3, c₁=(-2,7), c₂=(-2,0) ] & = 25+