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Parametric Equations

Parametric Equations

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Question 143

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 diagram showing a Cartesian coordinate system with x and y axes. A circle C2 is centered at the origin with a radius of 5. An ellipse C1 is also centered at the origin, with a horizontal semi-axis of 6 and a vertical semi-axis of 2*sqrt(5). The ellipse C1 intersects the circle C2 at four distinct points, one in each quadrant.

Find the Cartesian coordinates of the points of intersection.

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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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