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Parametric Equations

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Question 44

A curve C1 C_1\,C1​ with parametric equations

x=7cos⁡t,y=26sin⁡t0≤t<2π x = 7 \cos t, \quad y = 2\sqrt{6} \sin t \quad 0 \leq t < 2\pi x=7cost,y=26​sint0≤t<2π

meets the circle C2 C_2\,C2​ at four distinct points with Cartesian coordinates

(1435,2785),(1435,−2785),(−1435,2785),(−1435,−2785) \left(\frac{14\sqrt{3}}{5}, \frac{2\sqrt{78}}{5}\right),\quad \left(\frac{14\sqrt{3}}{5}, -\frac{2\sqrt{78}}{5}\right),\quad \left(-\frac{14\sqrt{3}}{5}, \frac{2\sqrt{78}}{5}\right),\quad \left(-\frac{14\sqrt{3}}{5}, -\frac{2\sqrt{78}}{5}\right) (5143​​,5278​​),(5143​​,−5278​​),(−5143​​,5278​​),(−5143​​,−5278​​)

as shown in the diagram.

A Cartesian diagram shows x and y axes with an ellipse C1 and a circle C2 centred at the origin, intersecting once in each quadrant.

Find the equation of the circle C2C_2C2​.

[2]
Markscheme

Parametric Equations Questions

  1. A Level
  2. /Maths
  3. /Parametric Equations

215 exam-style questions on Edexcel A Level Maths Parametric Equations, covering 8.1 Parametric Equations, 8.2 Using Trigonometric Identities, 8.3 Curve Sketching, 8.4 Points of Intersection, and 8.5 Modelling with Parametric Equations. Each one has a worked solution and a mark scheme showing where the marks go.

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