### Circles

- The equation of a ‘
**standard**’ circle is x^{2}+y^{2}=r^{2}.

This circle has a**radius**of r, and its centre is the**origin**(0,\ 0).

E.g. The right shows the graph of the circle with equation x^{2}+y^{2}=4.

Note: Be careful here that the radius is 2, and not 4 as it should be r^{2}=4,\ r=2.

- By definition r>0 as it signifies the radius of the circle. However, if we observe the equation, r can be negative too (the interpretation of the negative sign will involve a concept called ‘
**vectors**’). - As we can see, x and y both have a
**range**of [-r,\ r].