Edexcel F1 2015 January — Question 4

Exam BoardEdexcel
ModuleF1 (Further Pure Mathematics 1)
Year2015
SessionJanuary
TopicConic sections

4. The parabola \(C\) has cartesian equation \(y ^ { 2 } = 12 x\) The point \(P \left( 3 p ^ { 2 } , 6 p \right)\) lies on \(C\), where \(p \neq 0\)
  1. Show that the equation of the normal to the curve \(C\) at the point \(P\) is $$y + p x = 6 p + 3 p ^ { 3 }$$ This normal crosses the curve \(C\) again at the point \(Q\).
    Given that \(p = 2\) and that \(S\) is the focus of the parabola, find
  2. the coordinates of the point \(Q\),
  3. the area of the triangle \(P Q S\).