Hyperbolic curves are a type of mathematical curve that can be described by hyperbolas, which are defined as the set of points where the difference of the distances to two fixed points (foci) is constant. These curves are commonly found in various fields, including physics and engineering, where they can represent certain types of motion or trajectories. In geometry, hyperbolic curves are part of the broader category of conic sections, which also includes circles, ellipses, and parabolas. The study of hyperbolic curves is essential in understanding concepts related to non-Euclidean geometry and has applications in areas such as astronomy and navigation.