  Given a finite set of non-collinear points in the plane, there exists a line
that passes through exactly two points. Such a line is called an ordinary line.
An efficient algorithm for computing such a line was proposed by Mukhopadhyay
et al. In this note we extend this result in two directions. We first show how
to use this algorithm to compute an ordinary conic, that is, a conic passing
through exactly five points, assuming that all the points do not lie on the
same conic. Both our proofs of existence and the consequent algorithms are
simpler than previous ones. We next show how to compute an ordinary hyperplane
in three and higher dimensions.
