The graph of a circle with centre (0, 0) and radius r is given by the equation:
x^{2} + y^{2} = r^{2}
Sketching Circles
The basic circleIf the equation is in the form x^{2} + y^{2} = r^{2} the following method should be used:
Example 1 Example 2Sketch the graph of x^{2} + y^{2} = 25 Sketch the graph of x^{2} + y^{2} = 8 Radius = √25
Centre is (0, 0)Radius = √ 8 = 2.8 (to 2 sig.fig.)
Centre is (0, 0)
The centre is not the origin
In a similar manner to parabolas and cubics the basic circle can be transformed.
The most common transformation is when the centre of the circle is not the origin.
The graph of a circle with centre (a, b) and radius r is given by the equation:

Example Sketch the graph of (x − 2)^{2} + (y + 3)^{2} = 9
Radius = √ 9 = 3 Centre is (2, 3) 