Mathematics 2009 JAMB Past Questions - Question 30: Find the locus of a particle which moves in the first quadrant so that it is equidistant from the lines x=0 and y=0 (where k is a constant )

Correct Answer

D

Explanation

The locus of a particle that is equidistant from the lines x=0 and y=0 in the first quadrant can be found by considering the distances from the particle to each line.Let's denote the coordinates of the particle as (x, y). The distance from the particle to the line x=0 is simply x, and the distance from the particle to the line y=0 is y.Since the particle is equidistant from both lines, we have:x = yThis equation represents a line in the first quadrant where the x-coordinate is equal to the y-coordinate. This line passes through the origin (0, 0) and has a slope of 1.Therefore, the locus of the particle is the line y = x, where x and y are both positive in the first quadrant.