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Parametric Equations

Parametric Equations

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Question 88

A curve C1 C_1\,C1​ with parametric equations

x=6cos⁡t,y=25sin⁡t0≤t<2π x = 6 \cos t, \quad y = 2\sqrt{5} \sin t \quad 0 \leq t < 2\pi x=6cost,y=25​sint0≤t<2π

meets the circle C2 C_2\,C2​ with equation

x2+y2=25 x^2 + y^2 = 25 x2+y2=25

at four distinct points as shown in the diagram.

A Cartesian diagram shows a circle C₂ and an ellipse C₁ centred at the origin and intersecting at four points, one in each quadrant.

a.

Show that the Cartesian equation of C1 C_1\,C1​ is

x236+y220=1 \frac{x^2}{36} + \frac{y^2}{20} = 1 36x2​+20y2​=1
[2]
b.

Find the Cartesian coordinates of the points of intersection.

[4]
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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