Edexcel FP1 2015 June — Question 5

Exam BoardEdexcel
ModuleFP1 (Further Pure Mathematics 1)
Year2015
SessionJune
TopicConic sections

5. The rectangular hyperbola \(H\) has equation \(x y = 9\) The point \(A\) on \(H\) has coordinates \(\left( 6 , \frac { 3 } { 2 } \right)\).
  1. Show that the normal to \(H\) at the point \(A\) has equation $$2 y - 8 x + 45 = 0$$ The normal at \(A\) meets \(H\) again at the point \(B\).
  2. Find the coordinates of \(B\).