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

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