Any conic section can be defined as the locus of points whose distances to a point (the focus) and a line (the directrix) are in a constant ratio. That ratio is called the eccentricity, commonly denoted as e.
The eccentricity can also be defined in terms of the intersection of a plane and a
where β is the angle between the plane and the horizontal and α is the angle between the cone's slant generator and the horizontal. For the plane section is a circle, for a parabola. (The plane must not meet the vertex of the cone.)
The linear eccentricity of an ellipse or hyperbola, denoted c (or sometimes f or e), is the distance between its center and either of its two