Question

The ends of a rod of length l move on two mutually perpendicular lines. Find the locus of the point on the rod which divides it in the ratio 1:2.

Answer 1

Let the two mutually perpendicular lines be x and y-axes and P(x₀, y₀) be any point on the locus. Let AB denote the corresponding position of the rod such that AP/BP = 2, where we have A(a, 0) and B(0, b). Then

l² = AB² = a² + b²

y₀ = 2b + 0/3; x₀ = 2(0) + 1(a)/3

Therefore,

The equation of locus is