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9 marksCo-ordinate Geometry

CAPE Pure Mathematics Unit 1 · May/June 2008 · Paper 2 · Question 4(a)(ii)

In the Cartesian plane with origin O, the coordinates of points P and Q are (-2, 0) and (8, 8) respectively. The midpoint of PQ is M.

Hence, or otherwise, find the coordinates of the centre of the circle through P, O and Q.

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Other parts of this question

  1. 4(a)(i)Find the equation of the line which passes through M and is perpendicular to PQ.[8 marks]
  2. 4(b)(i)Prove that the line y = x + 1 is a tangent to the circle x² + y² + 10x – 12y + 11 = 0.[6 marks]
  3. 4(b)(ii)Find the coordinates of the point of contact of this tangent to the circle.[2 marks]

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