There are two versios for the equation of a circle. A simplified version where the center of the circle is at coordinates (0, 0) and a generic version where the centre of the circle can be anywhere on the graph.

Example I: Equation of a circle with radius = 4 at (0,0)

For the more generic equation of a circle where the circle centre is not at (0, 0) then this is as follows

Example II: Equation of a circle with radius = 4 at (–2, 3)

NoteWhen replacing the x and y coordinates into the equation, YOU MUST FLIP THE SIGNS of the x and y values.

In the above example, the x-coordinate of the centre circle is –2 so in the equation we write +2; and the y-coordinate is +3 so we write –3 in the equation.