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4 marksCo-ordinate Geometry

CAPE Pure Mathematics Unit 1 · May/June 2013 · Paper 2 · Question 4(b)

Show that the Cartesian equation of the curve that has the parametric equations x = t² + t, y = 2t – 4

is 4x = y² + 10y + 24.

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Other parts of this question

  1. 4(a)(i)Show that the centre and the radius of the circle, C, are (3, 2) and 3, respectively.[3 marks]
  2. 4(a)(ii)a)Find the equation of the normal to the circle C at the point (6, 2).[3 marks]
  3. 4(a)(ii)b)Show that the tangent to the circle at the point (6, 2) is parallel to the y-axis.[3 marks]
  4. 4(c)(i)Express the vectors AB and BC in the form xi + yj + zk.[3 marks]
  5. 4(c)(ii)Show that the vector r = − 16j - 8k is perpendicular to the plane through A, B and C.[5 marks]
  6. 4(c)(iii)Hence, find the Cartesian equation of the plane through A, B and C.[4 marks]

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