Formed when a plane intersects both parts of a double cone. The collection of all points such that the difference of the distances from a point, (x, y), on the hyperbola to two fixed points, the foci, is constant. Each hyperbola has two curves or branches that do not intersect. The vertices of a hyperbola are intersected by the line drawn through the two foci. The line segment that connects the two vertices is called the transverse axis, and the midpoint of this segment is the center of the hyperbola. The conjugate axis is perpendicular to the transverse axis and helps to shape the hyperbola. Its midpoint is also the center of the hyperbola.  

Khan Academy Practice:

• Intro to Hyperbola

• Finding the Vertices

• Finding the Foci

• Hyperbola not at the Origin