A hyperbola is a geometric shape consisting of all points where the difference between the distances to two fixed points (foci) is a constant. The foci lie on the transverse axis, which connects the two vertices where the curve turns. Asymptotes are lines the hyperbola approaches but never touches. To graph a hyperbola, identify its foci, vertices, and asymptotes, and be able to write the standard equation given properties of its foci and vertices.