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 {\em 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 {\em ordinary conic}, that is, a conic passing through exactly five points, assuming that all the points do not lie onthe same conic. Our proof of existence and the consequent algorithm is simpler than previous ones. We also show how to compute an ordinary hyperplane in threeand higher dimensions.