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3 marksCo-ordinate Geometry

CAPE Pure Mathematics Unit 1 · May/June 2011 · Paper 2 · Question 3(b)(iii)

The line L has equation x - y + 1 = 0 and the circle C has equation x² + y² – 2y - 15 = 0.

Find the constants a, b and c such that x = b + a cos θ and y = c + a sin θ are parametric equations (in parameter θ) of C.

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Other parts of this question

  1. 3(a)(i)Find the value of (a+b)⋅(a-b).[5 marks]
  2. 3(a)(ii)If 2b - a = 11i, determine the possible values of a and b.[5 marks]
  3. 3(b)(i)Show that L passes through the centre of C.[2 marks]
  4. 3(b)(ii)If L intersects C at P and Q, determine the coordinates of P and Q.[3 marks]
  5. 3(b)(iv)Another circle C₂, with the same radius as C, touches L at the centre of C. Find the possible equations of C₂.[7 marks]

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