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3 marksCo-ordinate Geometry

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

A curve is given by the parametric equations x = 2 + 3 sin t, y = 3 + 4 cos t.

Show that the Cartesian equation of the curve is (x-2)²/9 + (y-3)²/16 = 1.

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Other parts of this question

  1. 4(a)(i)The line x - 2y + 4 = 0 cuts the circle, x² + y² - 2x - 20y + 51 = 0 with centre P, at the points A and B. Find the coordinates of P, A and B.[6 marks]
  2. 4(a)(ii)b)Find the equation of circle C.[2 marks]
  3. 4(a)(ii)c)Find the distance, | PQ |, between the centres.[3 marks]
  4. 4(a)(ii)d)Find the distance | PM | if PQ cuts AB at M.[4 marks]
  5. 4(b)(ii)Show that every point on the curve lies within or on the circle (x – 2)² + (y - 3)² = 25.[5 marks]

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