Next exam for C2: Wednesday 23rd May

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.