Question

P, Q, R and S are the points of intersection with the co-ordinate axes of the lines px + qy = pq and qx + py = pq, then (p, q > 0)

• A. P, Q, R, S from a parallelogram
• B. P, Q, R, S from a rhombus
• C. P, Q, R, S are concylic
• D. None of these

Answer 1

Answer: (C)

P, Q, R, S are concylic

Answer 2

If the points of intersection of two lines with co-ordinate axes be concylic, then product of intercepts on x-axis is equal to product of intercepts on y-axis by these lines. This is a geometry property. The intercepts on x-axis are b and a whose product is pq. Also the intercepts on y-axis are p, q whose product is also pq. Hence the four points are concylic.