GCSEMathsEdexcelRevision Notes2. AlgebraEquation of a CircleEquation of a Circle

Equation of a Circle (Edexcel GCSE Maths)

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Equation of a Circle

What is the equation of a circle?

  • A circle centered on the origin with radius r has equation x2 + y2 = r2
  • (a, b) lies on the circle if a2 + b2 = r2
    • If a2 + b2 < r2 then (a, b) lies inside the circle
    • If a2 + b2 > r2 then (a, b) lies outside the circle
  • The circle cuts the x- and y-axes at ±r (“plus or minus r”)
  • The diameter = 2r and the circumference = 2πr

Exam Tip

  • if asked for the radius, don't forget to square root r2
    • e.g. for x2 + y2 = 10, the radius is √10, not "10"

Worked example

Circles - Equation & Graphs Worked Example 1, downloadable IGCSE & GCSE Maths revision notesCircles, IGCSE & GCSE Maths revision notes

Circles - Equation & Graphs Worked Example 2, downloadable IGCSE & GCSE Maths revision notes

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    Amber

    Author: Amber

    Amber gained a first class degree in Mathematics & Meteorology from the University of Reading before training to become a teacher. She is passionate about teaching, having spent 8 years teaching GCSE and A Level Mathematics both in the UK and internationally. Amber loves creating bright and informative resources to help students reach their potential.