GCSEMathsAQARevision Notes2. AlgebraEquation of a CircleEquation of a Circle

Equation of a Circle (AQA 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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    Daniel I

    Author: Daniel I

    Daniel has taught maths for over 10 years in a variety of settings, covering GCSE, IGCSE, A-level and IB. The more he taught maths, the more he appreciated its beauty. He loves breaking tricky topics down into a way they can be easily understood by students, and creating resources that help to do this.