The representation of Bézier curves in Parallel Planes Coordinates is studied and implemented, adding to the general collection of objects that can be represented using Parallel Planes Coordinates. Conic sections are investigated as a special set of rational Bézier curves. The representative properties of Bézier curves in Parallel Planes Coordinates are presented. Coordinate plane ordering schemes are investigated. A shape distortion minimization scheme is developed and implemented for more meaningful representations. Representations of Bézier curves are based on the new scheme.