• Expanding the brackets in the standard form and collecting the terms gives the general form:

x² + y² + 2g x + 2f y + c = 0

• From this form we obtain the elements of the circle as follows:

Condition for a real circle

• For the equation to represent a real circle we need g² + f² − c > 0.
• If this value is zero, the circle reduces to a single point.
• If it is negative, no point satisfies the equation.