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

## 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.

### 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 |
---|---|---|---|

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 |

C Coordinate Geometry in (x,y) | C2 Circles | Circles | |

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 |