We study circles, ellipses, and hyperbolas.

A circle is a locus of points in a plane that are a fixed distance from a given point in that plane. The fixed distance is the radius of the circle and the given point is the center.

An ellipse is defined geometrically as: for a given two points F1 and F2 in a plane, for any positive constant k greater than the distance F1F2, the locus of all points P in the plane such that PF1 + PF2 = k.

A hyperbola is defined as: for a given two points F1 and F2 in a plane, for any positive contstant k, the locus of all points P in the plane such that |PF1 – PF2| = k.

We study the common properties of these three kinds.