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JAMB Mathematics 2007 Question 43

Question 43

Loci

A particle P moves between points S and T such that angle SPT is always constant. Find the locus of P.

  1. A.It is a semi-circle with ST as diameter.
  2. B.It is a perpendicular bisector of ST.
  3. C.It is a quadrant of a circle with ST as diameter.
  4. D.It is a straight line perpendicular to ST.
Show the answer and explanation

Answer: A (It is a semi-circle with ST as diameter.)

Explanation

Points that see ST at a fixed angle lie on a circular arc through S and T; of the choices, the semicircle on ST as diameter is the arc (the case where the angle is 90°).