Equation of a Circle

Every circle can be written as an equation in the form:

$(x-h)^2+(y-k)^2=r^2$

in which the coordinate $(h,k)$ is the center of the circle and $r$ is the radius of the circle. Any point $(x,y)$ that makes the equation true is on the circle.

When you are given the equation of a circle, you can pull a lot of information from that equation, and even draw the circle based on the information that you pull out.

Example: 

$(x-3)^2+(y-2)^2=16$

Looking at this equation, you know that the center of the circle is $(3,2)$.