Concept:The locus of points that are equidistant from two fixed points P and Q is the perpendicular bisector of the segment
PQ.
Explanation:A locus is the path of a moving point that satisfies a given condition.
Here, the moving point X is equidistant from the points P and Q which determine the line
PQ, so
XP=XQ.
Therefore, X must lie on the straight line that passes through the midpoint of
PQ and meets
PQ at a right angle.
That straight line is called the perpendicular bisector of
PQ.
A circle centred at P or at Q would require a constant distance from only one point, so options A and C are not correct.
A pair of lines parallel to
PQ represents a constant distance from the line itself, not equal distances from the two fixed points P and Q.
Hence, the required locus is a perpendicular line to
PQ.
Answer:D. perpendicular line to PQ