Hiperbólicas

Hiperbólicas is a term derived from the Spanish word "hiperbólica," which translates to "hyperbolic" in English. This term is primarily used in mathematics to refer to a type of conic section. A hyperbola is defined as the set of all points in a plane where the absolute difference of the distances to two fixed points, called foci, is constant. This constant difference is equal to the distance between the two vertices of the hyperbola.

The geometric shape of a hyperbola consists of two separate, mirror-image curves. These curves extend infinitely. The standard equation of a hyperbola centered at the origin with a horizontal transverse axis is (x^2 / a^2) - (y^2 / b^2) = 1, where 'a' is the distance from the center to a vertex, and 'b' is related to the conjugate axis. If the transverse axis is vertical, the equation becomes (y^2 / a^2) - (x^2 / b^2) = 1.

Hyperbolas have several important properties. They possess asymptotes, which are lines that the branches of the hyperbola approach infinitely closely but never intersect. The eccentricity of a hyperbola is always greater than 1, indicating its open and diverging nature.

In physics and astronomy, hyperbolic trajectories describe the paths of objects that have enough energy to escape a gravitational influence, such as comets passing the Sun. The term "hiperbólicas" in a non-mathematical context might metaphorically refer to something exaggerated or excessively amplified, similar to how hyperbolic curves diverge greatly.