CAIE P1 2010 November — Question 10

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2010
SessionNovember
TopicStraight Lines & Coordinate Geometry

10 The equation of a curve is \(y = 3 + 4 x - x ^ { 2 }\).
  1. Show that the equation of the normal to the curve at the point \(( 3,6 )\) is \(2 y = x + 9\).
  2. Given that the normal meets the coordinate axes at points \(A\) and \(B\), find the coordinates of the mid-point of \(A B\).
  3. Find the coordinates of the point at which the normal meets the curve again.