Find the equation of circle passing through the points of intersection of x2+y2=6 and x2+y2−6x+8=0 and the point (1,1)
S1=x2+y2−6=0
S2=x2+y2−6x+8=0
S1+k(S2−S1)=0
S2−S1=−6x+14
x2+y2−6+k(−6x+14)=0
(1,1)
12+12−6+k(−6(1)+14)=0
−4+8k=0
∴k=12
⇒(2)(x2+y2−6)+(1)(−6x+14)=0
2x2+2y2−12−6x+14=0
2x2+2y2−6x+2=0
∴x2+y2−3x+1=0 is the required equation.