AP EAMCET Engineering 21 Apr 2019 Shift 1 Paper

The equation of common chord of given circles is
2x+1=0
The equation of circle passing through the intersection of given circles is,
(x2+y2+2x+3y+1)+λ(x2+y2+4x+3y+2)‌‌=0
x2(1+λ)+y2(1+λ)+(1+2λ)2x+3y(1+λ)+1+2λ‌‌=0
x2+y2+(‌

1+2λ

1+λ

)2x+3y+‌

1+2λ

λ+1

‌‌=0.....(I)
since 2x+1=0 is diameter of circle so
−2(−‌

2λ+1

1+λ

)+1‌‌=0
−4λ−2+λ+1‌‌=0
−3λ−1‌‌=0
λ‌‌=−‌

1

3

The from equation (I)
x2+y2+(‌

1− 2 3

1−‌ 1 3

)2x+3y+‌

1− 2 3

−‌ 1 3 +1

=0
x2+y2+(‌

‌ 1 3

2 3

)2x+3y+‌

‌ 1 3

2 3

=0
x2+y2+x+3y+‌

1

3

2x2+2y2+2x+6y+1=0