The points `P (cp, c/p)` and `Q (cq, c/q)`, where `|\ p\ | ≠ |\ q\ |`, lie on the rectangular hyperbola with equation `xy = c^2.`
The tangent to the hyperbola at `P` intersects the `x`-axis at `A` and the `y`-axis at `B`. Similarly, the tangent to the hyperbola at `Q` intersects the `x`-axis at `C` and the `y`- axis at `D`.
- Show that the equation of the tangent at `P` is `x + p^2 y = 2cp.` (2 marks)
- Show that `A, B and O` are on a circle with centre `P.` (2 marks)
- Prove that `BC` is parallel to `PQ.` (1 mark)