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JAMB Mathematics 1978 Question 40

Question 40

Loci

The locus of all points having a distance of l units from each of the two fixed points a and b is:

  1. A.a line parallel to the line ab
  2. B.a line perpendicular to the line ab through the mid-point of ab
  3. C.a circle through a and b with centre at the mid-point of ab
  4. D.a circle with centre at a and passes through b
  5. E.a circle in a plane perpendicular to ab and centre at the mid-point of the line ab.
Show the answer and explanation

Answer: E (a circle in a plane perpendicular to ab and centre at the mid-point of the line ab.)

Explanation

Points at distance l from a lie on a sphere of radius l about a, and likewise for b. Two equal spheres meet in a circle centred at the mid-point of ab, in the plane perpendicular to ab.