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# The locus of a point which is equidistant from the line PQ forms a

### Question

The locus of a point which is equidistant from the line PQ forms a

### Options

A) circle centre P

B) pair of parallel lines each opposite to PQ

C) circle centre Q

D) perpendicular line to PQ

### Explanation:

The locus of points at a fixed distance from the point P is a circle with the given P at its centre.
The locus of points at a fixed distance from the point Q is a circle with the given point Q at its centre
The locus of points equidistant from two points P and Q i.e line PQ is the perpendicular bisector of the segment determined by the points
Hence, The locus of a point which is equidistant from the line PQ forms a perpendicular line to PQ

## Dicussion (1)

• The locus of points at a fixed distance from the point P is a circle with the given P at its centre.
The locus of points at a fixed distance from the point Q is a circle with the given point Q at its centre
The locus of points equidistant from two points P and Q i.e line PQ is the perpendicular bisector of the segment determined by the points
Hence, The locus of a point which is equidistant from the line PQ forms a perpendicular line to PQ