The angles of elevation of the tops of two pillars of heights h and 2h from a point P on the line joining the feet of the two pillars are complementary. If the distances of the foot of the pillars from the point P are x and y respectively, then which one of the following is correct?

Let the angles of elevation be θ and (90° - θ) since they're complementary. For pillar of height h: tan(θ) = h/x. For pillar of height 2h: tan(90° - θ) = cot(θ) = 2h/y. Since tan(θ) × cot(θ) = 1, we have (h/x) × (2h/y) = 1, which gives 2h² = xy. Option A has x²y which is dimensionally inconsistent. Option B has xy² which is also incorrect. Option D has x²y² which gives the wrong dimensions. The key is recognizing that complementary angles give tan(θ) × cot(θ) = 1.