This
Introduction.
Geometry. Different definitions:
- as plane sections of a conical surface
- in terms of eccentricity
- in terms of distances from the foci
Analytical geometry and algebra. If the two independent variables \(x\), \(y\) represent the Cartesian coordinates of points in the plane, the second-degree polynomial equation
\[ A x^2 + B x y + C y^2 + D x + E y + F = 0 \ , \]
when it admits real solutions, defines the set of points of a regular or degenerate conic section, see Math:Analytic Geometry:Conics and Quadratic Forms.
Geometric properties.
…
Physics.
Gravitation, trajectories in the two-body problem, see Physics:Mechanics:Dynamics:Central motions
Trajectories of two electric charges, as in the
Physics:XX Century Physics:Rutherford–Geiger–Marsden scattering experiment, through which the Rutherford atomic model was formulated. This model predicts that the atom is mostly empty space with a positively charged nucleus. The three scientists bombarded a thin gold foil with positively charged () particles and observed a scattering pattern compatible with hyperbolic trajectories—those followed by a charged particle under the electric field generated by another point charge of the same sign, kept at rest.