| Exam Board | Edexcel |
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| Module | FP1 (Further Pure Mathematics 1) |
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| Topic | Straight Lines & Coordinate Geometry |
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7. The point \(P \left( 2 p , \frac { 2 } { p } \right)\) and the point \(Q \left( 2 q , \frac { 2 } { q } \right)\), where \(p \neq - q\), lie on the rectangular hyperbola with equation \(x y = 4\).
The tangents to the curve at the points \(P\) and \(Q\) meet at the point \(R\).
Show that at the point \(R\),
$$x = \frac { 4 p q } { p + q } \text { and } y = \frac { 4 } { p + q }$$
[*P5 June 2002 Qn 7]