OCR H240/02 — Question 5 8 marks

Exam BoardOCR
ModuleH240/02 (Pure Mathematics and Statistics)
Marks8
TopicAreas Between Curves

5 The diagram shows the circle with centre O and radius 2, and the parabola \(y = \frac { 1 } { \sqrt { 3 } } \left( 4 - x ^ { 2 } \right)\).
\includegraphics[max width=\textwidth, alt={}, center]{f2f45d6c-cfdc-455b-ab08-597b06a69f36-06_838_970_1059_280} The circle meets the parabola at points \(P\) and \(Q\), as shown in the diagram.
  1. Verify that the coordinates of \(Q\) are \(( 1 , \sqrt { 3 } )\).
  2. Find the exact area of the shaded region enclosed by the \(\operatorname { arc } P Q\) of the circle and the parabola.
    [0pt] [8]