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5 marksCo-ordinate Geometry

CAPE Pure Mathematics Unit 1 · May/June 2000 · Paper 2 · Question 3(b)(iii)

The curve C has parametric equations x = 3 + 5 sin θ, y = 4 + 5 cos θ, where 0 ≤ θ ≤ 2π.

Find the equations of the tangent and normal to the curve, C, at the point given by θ = 0.

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Other parts of this question

  1. 3(a)(i)Express the complex number z = (11 - 2i) / (3 + 4i) in the form a + ib, where a and b are real numbers.[4 marks]
  2. 3(a)(ii)Hence, express z² and iz in a similar form.[3 marks]
  3. 3(a)(iii)Find the modulus and principal value of the argument of z, where -π < arg z ≤ π.[3 marks]
  4. 3(a)(iv)Find the exact distance between the points on the Argand diagram represented by z² and iz.[3 marks]
  5. 3(b)(i)Find the cartesian equation of the curve, C.[4 marks]
  6. 3(b)(ii)Describe the curve, C, in detail.[3 marks]

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