1. The problem statement, all variables and given/known data Prove that the chord joining the points P(cp, c/p) and Q(cq, c/q) on the rectangular hyperbola xy = c^2 has the equation x + pqy = c(p + q) The points P, Q, R are given on the rectangular hyperbola xy = c^2 . prove that (a) if PQ and PR are equally inclined to the axes of coordinates, then QR passes through the origin O. (b) if angle QPR is a right angle, then QR is perpendicular to the tangent at P 2. Relevant equations 3. The attempt at a solution I can prove the equation of the chord joining the 2 points, but I am having difficulty with (a). What does "inclined to the axes of coordinates" mean? If I interpret 2 lines "inclined to the axes of coordinates" to mean to 2 parallel lines I am unable to envisage 2 such lines where R and Q are not coincident so I think my interpretation is wrong. Also would the case where Q and R are coincident not reveal a counter example or does the wording of the question imply that the points are unique?