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

Correct answer is B

The locus of all points having a distance of 1 unit from each of the two fixed points. a and b is: a perpendicular to the (ab) through the mid-points ab