JAMB - Mathematics (2007 - No. 38)
A particle P moves between points S and T such that angles SPT is always constant of ST constant. Find the locus of P
It is a semi circle with ST as diameter
It is a perpendicular bisector of St
It is a quadrant of a circle with ST as diameter
It is a straight line perpendicular to ST
Paliwanag
When a particle P moves such that the angle ∠SPT is constant while ST remains fixed, it traces a circular path. Specifically, the locus of P is a semicircle because points on the circle subtended by the line segment ST maintain that angle.