Circles are described by the Cartesian equation:
\qquad \qquad (x-a)^2 + (y-b)^2 = r^2
where (a,b) is the centre and r is the radius of the circle.
The equation of the circle whose centre is at the origin is x^2+y^2=r^2
The equation of the unit circle whose centre is at the origin is x^2+y^2=1
Summary/Background
  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
Glossary
cartesian equation
An equation that shows a relationship between the x and y cartesian coordinates.
circle
a conic curve with equation (x-a)²+(y-b)²=r²
equation
A statement that two mathematical expressions are equal.
graph
A diagram showing a relationship between two variables.
The diagram shows a vertical y axis and a horizontal x axis.
The diagram shows a vertical y axis and a horizontal x axis.
origin
The point from where all measurements of coordinates are made; usually the point where the two axes of a graph cross.
union
The union of two sets A and B is the set containing all the elements of A and B.
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 | - |