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1.6 C: Coordinate geometry in the (x, y) plane

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Question 15

The curve C C\,C has parametric equations

x=t2−4x = t^2 - 4x=t2−4, y=t3−4ty = t^3 - 4ty=t3−4t, t∈Rt \in \mathbb{R}t∈R

a.

Show that C C\,C crosses itself at the origin, and state the two values of t t\,t for which C C\,C passes through the origin.

[4]
b.

Find an equation of the tangent to C C\,C at the point where t=2t = 2t=2.

[3]
c.

Hence write down an equation of the other tangent to C C\,C at the origin.

[1]
Markscheme

1.6 C: Coordinate geometry in the (x, y) plane Questions

  1. A Level
  2. /Maths
  3. /1.6 C: Coordinate geometry in the (x, y) plane

143 exam-style questions on AQA A Level Maths 1.6 C: Coordinate geometry in the (x, y) plane, covering 1.6.1 Equation of a straight line, 1.6.2 Coordinate geometry of the circle, 1.6.3 Parametric equations of curves (A-level only), and 1.6.4 Parametric equations in modelling (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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