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

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Question 10

The curve C C\,C has parametric equations

x=3cos⁡θx = 3\cos\thetax=3cosθ, y=2sin⁡θy = 2\sin\thetay=2sinθ, where 0≤θ<2π0 \leq \theta < 2\pi0≤θ<2π

a.

Show that a Cartesian equation for C C\,C is x29+y24=1\dfrac{x^2}{9} + \dfrac{y^2}{4} = 19x2​+4y2​=1.

The point P P\,P on C C\,C has parameter θ=π3\displaystyle \theta = \frac{\pi}{3}θ=3π​.

[2]
b.

Show that the tangent to C C\,C at P P\,P has equation

2x+33y=122x + 3\sqrt{3}y = 122x+33​y=12

[5]
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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