Conic Sections of Minkowski Diagrams

Just for kicks, let's define the conic sections on Minkowski Diagrams.

The first one's easy. A point is an event--the intersection of an event's past and future is itself.

A circle is the locus of future events (a time t from now) that a certain event will affect. It is also the locus of past events (a time t ago) that have affected a certain event.

An ellipse is similar to a circle. An ellipse is the locus of future events (a time t' from now) that a certain event will affect. It is also the locus of past events (a time t' ago) that have affected the event in question. t' indicates that time is now being kept be an obsever who is in relative motion to the event in question.

A parabola

A hyperbola is the locus of events on a certain x coordinate, a certain y coordiante, or any of a number of lines (in Flatland) that the event in question can affect or has been affected by.

Orientation in Space-Time