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5 marksCo-ordinate Geometry

CAPE Pure Mathematics Unit 1 · May/June 2002 · Paper 2 · Question 3(a)(ii)

A curve is given by the parametric equations x = 4t², y = 8t.

Show that the Cartesian equation of the tangent to the curve at the point P with parameter T is Ty = x + 4T².

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Other parts of this question

  1. 3(a)(i)Find dy/dx in terms of t.[4 marks]
  2. 3(a)(iii)The tangent in (ii) above meets the y-axis at the point Q and the x-axis at the point R. If O is the origin, show that the area of triangle OQR is 8T³ square…[6 marks]
  3. 3(b)Solve for x ∈ R the inequality (2x + 3) / (3x + 4) < 1.[10 marks]

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