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.
Summary/Background
- 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
![]() Circles can be displayed on your graphic
calculator, for example, on the TI-83: Select the Y= screen: Enter Y1 = ?(R -(X-A) )+BEnter Y2 = -?(R -(X-A) )+BThen 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 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 question appears in the following syllabi:
| Syllabus | Module | Section | Topic | Exam Year |
|---|---|---|---|---|
| AQA A-Level (UK - Pre-2017) | C1 | Coordinate geometry | Circles - geometry | - |
| AQA AS Maths 2017 | Pure Maths | Straight Lines and Circles | Circle Geometry | - |
| AQA AS/A2 Maths 2017 | Pure Maths | Straight Lines and Circles | Circle Geometry | - |
| CBSE XI (India) | Coordinate Geometry | Conic Sections | Circle, parabola, ellipse, hyperbola, point & straight line | - |
| CCEA A-Level (NI) | C2 | Coordinate geometry | Circles - geometry | - |
| Edexcel A-Level (UK - Pre-2017) | C2 | Coordinate geometry | Circles - geometry | - |
| Edexcel AS Maths 2017 | Pure Maths | Circles | Circle Geometry | - |
| Edexcel AS/A2 Maths 2017 | Pure Maths | Circles | Circle Geometry | - |
| Methods (UK) | M1 | Coordinate geometry | Circles - geometry | - |
| OCR A-Level (UK - Pre-2017) | C1 | Coordinate geometry | Circles - geometry | - |
| OCR AS Maths 2017 | Pure Maths | Lines and Circles | Circle Geometry | - |
| OCR MEI AS Maths 2017 | Pure Maths | Lines and Circles | Circle Geometry | - |
| OCR-MEI A-Level (UK - Pre-2017) | C1 | Coordinate geometry | Circles - geometry | - |
| Pre-Calculus (US) | C6 | Coordinate geometry | Circles - geometry | - |
| Pre-U A-Level (UK) | 2 | Coordinate geometry | Circles - geometry | - |
| Scottish (Highers + Advanced) | HM2 | Coordinate geometry | Circles - geometry | - |
| Scottish Highers | M2 | Coordinate geometry | Circles - geometry | - |
| Universal (all site questions) | C | Coordinate geometry | Circles - geometry | - |
| WJEC A-Level (Wales) | C2 | Coordinate geometry | Circles - geometry | - |


Circles can be displayed on your graphic
calculator, for example, on the TI-83:
-(X-A)
ALPHA R. You may also need to adjust the scaling to get a good display of the circle.