- #1
Appleton
- 91
- 0
Homework Statement
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
Homework Equations
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?