Circumference is the set of all points on a plane equidistant from a fixed point on that same plane, called the center of the circumference:

# Circumference Equations

## Reduced equation

Being **Ç**(a, b) the center and **P**(x, y) any point of the circumference, the distance of **Ç** The **P**(d_{CP}) is the radius of this circumference. So:

Therefore, **(x - a) ^{2} + (y - b)^{2} = r^{2}** It is the reduced circumference equation and allows you to determine the essential elements for constructing the circumference: the center coordinates and the radius.

Note: When the center of the circle is at the origin (C (0,0)), the circle equation is x^{2} + y^{2} = r^{2}.

## General equation

Developing the reduced equation, we get the general circumference equation:

As an example, let's determine the general equation of the center circumference. **Ç**(2,3) and radius r = 4.

The reduced circumference equation is:

(x - 2)^{2} + (y + 3)^{2} = 16

Developing the binomial squares, we have:

Next: Determination of Center and Radius