A hyperbola is a type of conic section formed by the intersection of a plane and a double cone. It consists of two separate curves called branches that open away from each other. The standard equation of a hyperbola can be expressed as (x^2/a^2) - (y^2/b^2) = 1 or (y^2/b^2) - (x^2/a^2) = 1, where a and b are constants that determine the shape and size of the hyperbola. Hyperbolas have unique properties, such as having asymptotes, which are lines that the branches approach but never touch. They are often found in various applications, including navigation systems, satellite communications, and physics, where they describe certain types of motion and trajectories.