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3 marksCo-ordinate Geometry

CAPE Pure Mathematics Unit 1 · May/June 2014 · Paper 2 · Question 4(a)(iii)

A and B are endpoints of the diameter L₁. Given that the coordinates of A are (1, 2) and that the diameters of a circle bisect each other.

A point, p, moves in the x - y plane such that its distance from C (2, 3) is always √2 units. Determine the locus of p.

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Other parts of this question

  1. 4(a)(i)Show that the coordinates of the centre of the circle, C, where L₁ and L₂ intersect are (2, 3).[3 marks]
  2. 4(a)(ii)determine the coordinates of B.[3 marks]
  3. 4(b)Determine the Cartesian equation of the curve, S.[6 marks]
  4. 4(c)(i)Express EACH of the vectors PQ, QR and RP in the form xi + yj + zk.[4 marks]
  5. 4(c)(ii)Hence, find the value of λ, given that PQR is right-angled with the side PQ as hypotenuse.[6 marks]

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