The locus of all points having a distance of 1 unit from each of the two fixed points a and b is

• A.a line parallel to the line ab
• B.a line perpendicular to the line ab through the mid-point of ab
• C.a circle through a and b with centre at the mid-point of ab
• D.a circle with centre at a and passes through b
• E.a circle in a plane perpendicular to ab and centre at the mid-point of the line ab