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5 marksCo-ordinate Geometry

CAPE Pure Mathematics Unit 1 · May/June 2023 · Paper 2 · Question 4(a)

Obtain the Cartesian equation of the curve given in parametric form x = 3\cos t and y = 4\sin t.

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  1. 4(b)The equation of a line is x = 2 + t, y = 1 - 3t and z = 4 + t, and the equation of a plane is x + 2y + z = 12. Determine the point of intersection of the line…[6 marks]
  2. 4(c)(i)Determine the vector equation of the plane which passes through (1, 5, -1) and which is perpendicular to the vector \begin{pmatrix}2\\4\\3\end{pmatrix}.[4 marks]
  3. 4(c)(ii)Hence, determine the coordinates of the point in the plane where y = 3 and z = 1.[3 marks]
  4. 4(d)Given that a line is parallel to the vector u = \begin{pmatrix}1\\-3\\1\end{pmatrix} and that the vector v = \begin{pmatrix}1\\2\\1\end{pmatrix} is normal to…[7 marks]

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