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(dCP) is the radius of this circumference. So:

Therefore, (x - a)2 + (y - b)2 = r2 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 x2 + y2 = r2.

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