In astrodynamics or celestial mechanics a hyperbolic trajectory is a Kepler orbit with the eccentricity greater than 1. Under standard assumptions a body traveling along this trajectory will coast to infinity, arriving there with hyperbolic excess velocity relative to the central body. Similarly to parabolic trajectory all hyperbolic trajectories are also escape trajectories. The specific energy of a hyperbolic trajectory orbit is positive. The shape of a hyperbolic trajectory is a hyperbola.
Planetary flybys, used for gravitational slingshots, can be described within the planet's sphere of influence using hyperbolic trajectories.
Read more about Hyperbolic Trajectory: Hyperbolic Excess Velocity, Velocity, Angle Between Approach and Departure, Distance of Closest Approach, Energy, Radial Hyperbolic Trajectory