  This paper first gives a brief overview over some interesting descriptions of
conic sections, showing formulations in the three geometric algebras of
Euclidean spaces, projective spaces, and the conformal model of Euclidean
space. Second the conformal model descriptions of a subset of conic sections
are listed in parametrizations specific for the use in the main part of the
paper. In the third main part the meets of lines and circles, and of spheres
and planes are calculated for all cases of real and virtual intersections. In
the discussion special attention is on the hyperbolic carriers of the virtual
intersections.
