Answer
$(x-h)^2+(y-k)^2=r^2$
Work Step by Step
A circle is defined as the set of all points in the plane that are a fixed distance from a given fixed point. The fixed distance is the radius of the circle, and the fixed point is called the center. If we let $r $ > 0 be the radius, ($h$, $k$) the center, and ($x$, $y$) represent any point on the circle, then ($x$, $y$) is r units from ($h$, $k$).
Applying the distance formula:
$$\sqrt{(x-h)^2+(y-k)^2} = r$$
Squaring both sides:
$$(x-h)^2+(y-k)^2=r^2$$
