The equation of the smallest circle passing through the points of intersection of the line $x+y-1=0$  and the circle $x^2+y^2=9$

detailed solution

Correct option is B

Given circle x2+y2=9.......(1)  and line if x+y−1=0............(2) The point of intersection of (1)&(2)   is (1)+λ(2)=0 ⇒x2+y2−9+λ(x+y−1)=0 ⇒x2+y2+λx+λy−λ−9=0.........(3) Centre (−λ2,−λ2) Since equation (3) is a smallest circle then equation (2)  is a diameter of the circle⇒Centre(−λ2,−λ2) lies on (2) −λ2,−λ2−1=0⇒λ=−1 Substituting λ=−1  in equation (3) ⇒x2+y2−9−(x+y−1)=0 ⇒x2+y2−x−y−8=0