OCR FP2 2013 June — Question 8

Exam BoardOCR
ModuleFP2 (Further Pure Mathematics 2)
Year2013
SessionJune
TopicPolar coordinates

8 The equation of a curve is \(x ^ { 2 } + y ^ { 2 } - x = \sqrt { x ^ { 2 } + y ^ { 2 } }\).
  1. Find the polar equation of this curve in the form \(r = \mathrm { f } ( \theta )\).
  2. Sketch the curve.
  3. The line \(x + 2 y = 2\) divides the region enclosed by the curve into two parts. Find the ratio of the two areas.