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4 marksCo-ordinate Geometry

CAPE Pure Mathematics Unit 1 · May/June 2015 · Paper 2 · Question 4(a)(i)

The circles C₁ and C₂ are defined by the parametric equations as follows: C₁: x = √10 cos θ – 3; y = √10 sin θ + 2. C₂: x = 4 cos θ + 3; y = 4 sin θ + 2.

Determine the Cartesian equations of C₁ and C₂ in the form (x – a)² + (y – b)² = r².

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Other parts of this question

  1. 4(a)(ii)Hence or otherwise, find the points of intersection of C₁ and C₂.[9 marks]
  2. 4(b)Show that the equation of the locus of the point P (x, y) is a circle.[12 marks]

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