Graphing a circle

A circle is easily created using a compass.  A circle is the set of points that are equidistant from a given center.

Using the Euclidean distance formula, we can an equation to represent a circle on the Cartesian coordinate system where the center is at $(0,0)$.

For radius $r$, the circle would be the set of points that have a Euclidean distance of $r$ from the $(0,0)$.

So, we start with the Euclidean Distance formula with: 

$r = \sqrt{(x-0)^2 + (y-0)^2}= \sqrt{x^2 + y^2}$

Squaring both sides gives us:

$$r^2 = x^2 + y^2$$