Edexcel F1 2017 June — Question 4

Exam BoardEdexcel
ModuleF1 (Further Pure Mathematics 1)
Year2017
SessionJune
TopicParametric equations

4. The rectangular hyperbola \(H\) has parametric equations $$x = 4 t , \quad y = \frac { 4 } { t }$$ The straight line with equation \(3 y - 2 x = 10\) intersects \(H\) at the points \(A\) and \(B\). Given that the point \(A\) is above the \(x\)-axis,
  1. find the coordinates of the point \(A\) and the coordinates of the point \(B\).
  2. Find the coordinates of the midpoint of \(A B\).