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9 marksCo-ordinate Geometry

CAPE Pure Mathematics Unit 1 · May/June 2000 · Paper 2 · Question 1(a)

A straight line y = 10 - 3x intersects a circle x² + y² + 2x - 16y = 0 at points A and B. Point A is in the first quadrant and B is in the second quadrant.

Find the coordinates of A and B.

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Other parts of this question

  1. 1(b)(i)Write down, in terms of θ and r, an expression for the area of S₁.[3 marks]
  2. 1(b)(ii)Write down, in terms of θ and r, an expression for the area of S₂.[4 marks]
  3. 1(b)(iii)Given that the area of S₂ is three times the area of S₁, show that 4θ = π + 2 sin θ.[4 marks]
  4. 1(b)(iv)Show that when r = 6, θ = π/3, the area of triangle PQR = 18√3.[5 marks]

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