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6 marksCo-ordinate Geometry

CAPE Pure Mathematics Unit 1 · May/June 2007 · Paper 2 · Question 3(a)(iii)

A circle, not drawn to scale, has centre C at (5, -4) and touches the y-axis at point D. The circle cuts the x-axis at points A and B. The tangent at B cuts the y-axis at point P. (Refer to Figure 1).

Determine the coordinates of the points A and B, at which the circle cuts the x-axis.

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Other parts of this question

  1. 3(a)(i)Determine the length of the radius of the circle.[2 marks]
  2. 3(a)(ii)Determine the equation of the circle.[1 mark]
  3. 3(a)(iv)Determine the equation of the tangent at B.[4 marks]
  4. 3(a)(v)Determine the coordinates of P.[2 marks]
  5. 3(b)Show by calculation that PD = PB.[5 marks]

More practice: the rest of this paper · more Co-ordinate Geometry questions · all CAPE Pure Mathematics Unit 1 past papers