Edexcel P1 2022 January — Question 10

Exam BoardEdexcel
ModuleP1 (Pure Mathematics 1)
Year2022
SessionJanuary
TopicCurve Sketching
TypeRational curve intersections

10. The curve \(C\) has equation $$y = \frac { 1 } { x ^ { 2 } } - 9$$
  1. Sketch the graph of \(C\). On your sketch
    • show the coordinates of any points of intersection with the coordinate axes
    • state clearly the equations of any asymptotes
    The curve \(D\) has equation \(y = k x ^ { 2 }\) where \(k\) is a constant. Given that \(C\) meets \(D\) at 4 distinct points,
  2. find the range of possible values for \(k\).