Equation of circle

Let there be a circle with center at point A1 (a; b) and radius R. Take an arbitrary point A (x; y) on the circle. Then, as can be seen from the figure, by the Pythagorean theorem



is the equation of a circle.
If the center of the circle is at the origin, i.e. a = 0 and b = 0, then the equation of a circle takes the form:



Conversely, any point A whose coordinates satisfy a given equation of a circle belongs to a circle.