OCR H240/01 2019 June — Question 5

Exam BoardOCR
ModuleH240/01 (Pure Mathematics)
Year2019
SessionJune
TopicImplicit equations and differentiation

5 A curve has equation \(x ^ { 3 } - 3 x ^ { 2 } y + y ^ { 2 } + 1 = 0\).
  1. Show that \(\frac { \mathrm { d } y } { \mathrm {~d} x } = \frac { 6 x y - 3 x ^ { 2 } } { 2 y - 3 x ^ { 2 } }\).
  2. Find the equation of the normal to the curve at the point ( 1,2 ).