What is the standard form of a hyperbola?

Hyperbolas always sit on a certain point that is either on the y or the x axis at -1. The center of the hyperbola remains at that point no matter how far the graph is created from the center or how far it is zoomed out.

On both the right and the left side or the top and the bottom of the hyperbola, it is at the exact same distance from the center. The distance that it is from the center at its vertices is predetermined and will vary from each hyperbola. The difference of the two foci of the hyperbola is fixed.