Locus of centre of circle bisecting circumference

Question

Please read before solving: I know the solution, I just don't understand what does bisecting the circumference means. A circumference is round, so how it can be bisected? Can someone explain (preferably by a figure)?

Answer 1

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.