CAIE Further Paper 1 2021 November — Question 6

Exam BoardCAIE
ModuleFurther Paper 1 (Further Paper 1)
Year2021
SessionNovember
TopicPolar coordinates

6 The curve \(C\) has polar equation \(r = 2 \cos \theta ( 1 + \sin \theta )\), for \(0 \leqslant \theta \leqslant \frac { 1 } { 2 } \pi\).
  1. Find the polar coordinates of the point on \(C\) that is furthest from the pole.
  2. Sketch C.
  3. Find the area of the region bounded by \(C\) and the initial line, giving your answer in exact form.