# Circle - Equation

## The equation for a circle

### Unit Circle

The equation of a unit circle - where the center of the circle is located in the origo of the coordinate system and the *radius = 1* - can be expressed as

*x ^{2} + y^{2} = 1 (1)*

### Standard Form

The standard form for the equation of a circle can be expressed as

*(x - a) ^{2} + (y - b)^{2} = r^{2} (2)*

*where *

*a = x coordinate position of the circle center*

*b = y coordinate position of the circle center*

*r = circle radius*

### General Form

The general form for the equation of a circle can be expressed as

*x ^{2} + y^{2} + A x + B y + C = 0 (3)*

*where *

*A, B, C = constants*

### Radius of circle

* r = ( a^{2} + b^{2} - C) ^{1/2}*

*(4)*

### Coordinates in the Circle Centre

*a = - A / 2 (5a)*

*b = - B / 2 (5b)*