OCR C1 2009 June — Question 11

Exam BoardOCR
ModuleC1 (Core Mathematics 1)
Year2009
SessionJune
TopicDifferentiation Applications
TypeTangent parallel to given line

11 The point \(P\) on the curve \(y = k \sqrt { x }\) has \(x\)-coordinate 4 . The normal to the curve at \(P\) is parallel to the line \(2 x + 3 y = 0\).
  1. Find the value of \(k\).
  2. This normal meets the \(x\)-axis at the point \(Q\). Calculate the area of the triangle \(O P Q\), where \(O\) is the point \(( 0,0 )\). RECOGNISING ACHIEVEMENT