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