P and Q are fixed points and X is a variable point that moves so that angle PXQ = 45°. What is the locus of x?
 

  • A A pair of straight lines parallel to PQ
  • B The perpendicular bisector of PQ
  • C An arc of a circle passing through P and Q
  • D A circle with diameter PQ
  • E The bisector of angle PXQ
jamb 1980mathematics

The correct answer is D. A circle with diameter PQ

The locus of a point X that moves so that the angle PXQ is always 45° is a circle with a diameter PQ. 

This is because, in a circle, the angle subtended by a diameter at any point on the circle is always 90°. 

Since 45° is half of 90°, the angle PXQ will be 45° for any point X on the circle.

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