Algebra/Circle

As you likely have learned before, a circle is defined as any set of points that is a fixed distance (the radius) from a fixed point (the center). To find a formula for this, suppose that the center is the point (a,b). According to the distance formula, the distance c from the point (a,b) to any other point (x, y) is:

$c^2=(x-a{)}^2+(y-b{)}^2$

By definition, a circle is the set of all points for a given value of c. We call this r and come up with the following equation for a circle: