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Let’s consider circle with  as circle’s center and  the circle’s radius.

The perimeter of circle is the geometric locus for the point , function of  and . The circle’s equation is the expression that it is true for any .

Using Pythagoras theorem for the right triangle we have:

[1]  where:

[2] 

[3] 

[4] 

By replacing the values we have for the different segment lines ([2], [3], and [4]) into [1] we get the general form of circle’s equation:

[5] 

When the center of the circle  is coincident with the Origin of the Cartesian Coordinate System  ( O(0, 0) ), and , [5] becomes:

[6]