Hyperbolas

Hyperbolas are basically, in definition, the set of all points (x,y) the difference of whose distances from two fixed points called the foci is always constant. The only difference between the definition of a hyperbola and an ellipse is that hyperbolas the distances from the foci and a point on the hyperbola is fixed while is the sum of the distances between foci and a point on the ellipse is fixed. There two branches of a hyperbola. Vertices are the points of a hyperbola where the line through the two foci intersects a hyperbola. The transverse axis is the line segment that connects the vertices. The exact midpoint on the transverse axis is the center of a hyperbola.

Below are the equations to a hyperbola: