Given circles are, x2+y2=4 and x2+y2 −2x+6y+1=0
The locus of the center of the circle bisects the circumferences of these two circles.
∴ Radical axis, S1−S2 =0
⟹(x2+y2−4)−(x2+y2−2x+6y+1)=0
2x−6y−5=0. This is a straight line.
The center lies on the line parallel to the above line.
⟹2x−6y+λ=0
This is a straight line.