  In this paper we introduce point-ellipse configurations and point-conic
configurations. We study some of their basic properties and describe two
interesting families of balanced point-ellipse, respectively point-conic
$6$-configurations. The construction of the first family is based on Carnot's
theorem, whilst the construction of the second family is based on the Cartesian
product of two regular polygons. Finally, we investigate a point-ellipse
configuration based on the regular $24$-cell.
