Two circles x2+y2=6  and x2+y2−6x+8=0  are given. Then the equation of the circle through their point of intersection and the point (1,1) is

Equation of the circle passing through the point of intersection of given circles x2+y2−6x+8+λ(x2+y2−6)=0   …..(1) This circle passes through (1,1) , then 1+1−6+8+λ(1+1−6)=0⇒λ=1 On putting the value of λ  in equation (1) then 2x2+2y2−6x+2=0 ⇒   x2+y2−3x+1=0 .This is the required equation of circle.