Two constructions for center of curvature at point on a conic [Howard Eves problems 14.1-3 (a) and (b)]

In this entry we present the justifications for two different constructions (compass and straightedge) of the center of curvature at a point on a conic as posed in Problems 14.1-3 (a) and (b) in Howard Eves' A Survey of Geometry Volume Two. The constructions make a nice application of the theory presented in the last entry on curvature at a point. The justifications are given in this attached paper, Constructions of Center of Curvature for Conics.