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5 marksCo-ordinate Geometry

CAPE Pure Mathematics Unit 1 · May/June 2006 · Paper 2 · Question 3(a)(ii)

By writing x + 1 = 3 sin θ, show that the parametric equations of this circle are x = -1 + 3 sin θ, y = 2 + 3 cos θ.

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Other parts of this question

  1. 3(a)(i)Find the coordinates of the centre and radius of the circle x² + 2x + y² – 4y = 4.[4 marks]
  2. 3(a)(iii)Show that the x-coordinates of the points of intersection of this circle with the line x + y = 1 are x = -1 + (3√2)/2.[4 marks]
  3. 3(b)Find the general solutions of the equation cos θ = 2 sin²θ – 1.[7 marks]

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