AP EAMCET Engineering 18 Sep 2020 Shift 1 Paper

The family of circles passes through the intersection of circles x2+y2=9 and line x+y=1 is
(x2+y2−9)+λ(x+y−1)=0
having centre (−‌

λ

2

,−‌

λ

2

)
For the smallest circle, the line x+y=1 must be diameter of the circle, so
−‌

λ

2

−‌

λ

2

=1⇒λ=−1
So, equation of the required circle is
x2+y2−x−y−8=0
or, (x2+y2−9)−(x+y−1)=0