Hyperbolas

A hyperbola is a type of curve formed by the intersection of a plane with two opposite cones, creating two separate branched shapes. In mathematics, it consists of points where the difference in distances to two fixed points called foci remains constant. Hyperbolas appear in nature and engineering, such as in the paths of satellites, navigation systems, and mirror designs. They are characterized by their open, mirror-like branches and distinctive asymptotes—lines they approach but never touch—giving them unique geometric and reflective properties.