Mathematical note: If the half-angle of the cone is
then the eccentricity of the intersection is
, where
is the angle of inclination of the plane. Its projection in the
plane is also a conic section, with focus at the origin and eccentricity
. Note that the eccentricity of the intersection and of its projection are equal for precisely two values of
, namely 0 and
, corresponding to eccentricities of 0 and 1, and thus to the circle and parabola, respectively.
