Conics are plane sections of a right-circular cone. These sections give birth to four different curves: circle, ellipse, parabola and hyperbola.
These curves represent the orbits solution of the 2-body problem. They were found by Newton, who invented the infinitesimal calculus to solve this precise problem. But to determine in which orbit the body will lie it is necessary to introduce another concept: the binding Energy of the object.

Conics are characterized by different values of the orbital parameters (click here to know more about the orbital parameters):

the major semiaxis, is easily defined for the ellipse and the circle. In the case of a parabola, it is considered infinite while for an hyperbola, it is considered negative.

the eccentricity, in the case of an ellipse, will assume values ranging from 0 (for the circle) to 1. While in the case of a parabola it will assume value =1 and will be superior to 1 in the case of an hyperbola.