Edexcel FP1 2009 January — Question 3

Exam BoardEdexcel
ModuleFP1 (Further Pure Mathematics 1)
Year2009
SessionJanuary
TopicConic sections

3. The rectangular hyperbola, \(H\), has parametric equations \(x = 5 t , y = \frac { 5 } { t } , t \neq 0\).
  1. Write the cartesian equation of \(H\) in the form \(x y = c ^ { 2 }\). Points \(A\) and \(B\) on the hyperbola have parameters \(t = 1\) and \(t = 5\) respectively.
  2. Find the coordinates of the mid-point of \(A B\).