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