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JAMB Mathematics 1986 Question 42

Question 42

Loci

If U and V are two distinct fixed points and W is a variable point such that UWV is a right angle, what is the locus of W?

  1. A.The perpendicular bisector of UV.
  2. B.A circle with UV as radius.
  3. C.A line parallel to the line UV
  4. D.A circle with the line UV as the diameter.
Show the answer and explanation

Answer: D (A circle with the line UV as the diameter.)

Explanation

The angle in a semicircle is a right angle, so every W with angle UWV = 90° lies on the circle with UV as diameter.