OCR Further Pure Core 2 Specimen — Question 9

Exam BoardOCR
ModuleFurther Pure Core 2 (Further Pure Core 2)
SessionSpecimen
TopicPolar coordinates

9 A curve has equation \(x ^ { 4 } + y ^ { 4 } = x ^ { 2 } + y ^ { 2 }\), where \(x\) and \(y\) are not both zero.
  1. Show that the equation of the curve in polar coordinates is \(r ^ { 2 } = \frac { 2 } { 2 - \sin ^ { 2 } 2 \theta }\).
  2. Deduce that no point on the curve \(x ^ { 4 } + y ^ { 4 } = x ^ { 2 } + y ^ { 2 }\) is further than \(\sqrt { 2 }\) from the origin.