The equation of a circle can be found using the centre and radius. The discriminant can determine the nature of intersections between two circles or a circle and a line to prove for tangency.

Example 1 Find the equation of a circle with radius 3 units and centre (0, 0). The radius, r = 3 and r 2 = 9, so the equation of the circle is x 2 + y 2 = 9.