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Circles are described by the Cartesian equation
\qquad (x-a)^2 + (y-b)^2 = r^2
where the centre is at (a,b) and the radius is r.

So, if you know the centre and radius of a circle you can write down its equation immediately.



  • The equation of a circle can be written as (x-a)²+(y-b)² = r²
  • This circle has centre at (a,b)
  • The circle has radius r
graphic calculator
circleCircles can be displayed on your graphic calculator, for example, on the TI-83:
Select the Y= screen:

Enter Y1 = √(Rsquare-(X-A)square)+B
Enter Y2 = -√(Rsquare-(X-A)square)+B
Then select the GRAPH screen. You can then choose different values for the constants A, B and R. For example, to make R = 4, press 4 store ALPHA R. You may also need to adjust the scaling to get a good display of the circle.

Software/Applets used on this page

This page uses jsMath
You can get a better display of the maths by downloading special TeX fonts from jsMath. In the meantime, we will do the best we can with the fonts you have, but it may not be pretty and some equations may not be rendered correctly.


cartesian equation

An equation that shows a relationship between the x and y cartesian coordinates.


a conic curve with equation (x-a)²+(y-b)²=r²


A statement that two mathematical expressions are equal.


A diagram showing a relationship between two variables.
The diagram shows a vertical y axis and a horizontal x axis.


The union of two sets A and B is the set containing all the elements of A and B.

Full Glossary List

This question appears in the following syllabi:

AQA A-Level (UK - Pre-2017)C1Coordinate geometryCircles - geometry
AQA AS Maths 2017Pure MathsStraight Lines and CirclesCircle Geometry
AQA AS/A2 Maths 2017Pure MathsStraight Lines and CirclesCircle Geometry
CBSE XI (India)Coordinate GeometryConic SectionsCircle, parabola, ellipse, hyperbola, point & straight line
CCEA A-Level (NI)C2Coordinate geometryCircles - geometry
C Coordinate Geometry in (x,y)C2 CirclesCircles
Edexcel A-Level (UK - Pre-2017)C2Coordinate geometryCircles - geometry
Edexcel AS Maths 2017Pure MathsCirclesCircle Geometry
Edexcel AS/A2 Maths 2017Pure MathsCirclesCircle Geometry
Methods (UK)M1Coordinate geometryCircles - geometry
OCR A-Level (UK - Pre-2017)C1Coordinate geometryCircles - geometry
OCR AS Maths 2017Pure MathsLines and CirclesCircle Geometry
OCR MEI AS Maths 2017Pure MathsLines and CirclesCircle Geometry
OCR-MEI A-Level (UK - Pre-2017)C1Coordinate geometryCircles - geometry
Pre-Calculus (US)C6Coordinate geometryCircles - geometry
Pre-U A-Level (UK)2Coordinate geometryCircles - geometry
Scottish (Highers + Advanced)HM2Coordinate geometryCircles - geometry
Scottish HighersM2Coordinate geometryCircles - geometry
Universal (all site questions)CCoordinate geometryCircles - geometry
WJEC A-Level (Wales)C2Coordinate geometryCircles - geometry