  Conics and Cartesian ovals are very important curves in various fields of
science. Also aspheric curves based on conics are useful in optics. Superconic
curves recently suggested by A. Greynolds are extensions of both conics and
Cartesian ovals and have been applied to optics while they are not extensions
of aspheric curves based on conics.
  In this work, we investigate another kind of superconic curves that are
extensions of not only conics and Cartesian ovals but also aspheric curves
based on conics. Moreover, the superconic curves are represented in explicit
form while Greynolds' superconic curves are in implicit form.
