Edexcel FP1 2010 June — Question 8

Exam BoardEdexcel
ModuleFP1 (Further Pure Mathematics 1)
Year2010
SessionJune
TopicConic sections

8. The rectangular hyperbola \(H\) has equation \(x y = c ^ { 2 }\), where c is a positive constant. The point \(A\) on \(H\) has \(x\)-coordinate \(3 c\).
  1. Write down the \(y\)-coordinate of \(A\).
  2. Show that an equation of the normal to \(H\) at \(A\) is $$3 y = 27 x - 80 c$$ The normal to \(H\) at \(A\) meets \(H\) again at the point \(B\).
  3. Find, in terms of \(c\), the coordinates of \(B\).