Most corneal topographers are based on the Placido disk, which is consists of a set of concentric rings illuminated in black and white. Each luminous ring is projected onto the corneal surface and its image produced by reflection is captured by a camera. When the corneal surface is symmetrical and aligned with respect to the optical axis of the corneal topographer, the image consists of concentric rings; therefore, displacements occur only in the radial direction. However, if the cornea lacks revolution symmetry, the image suffers deformations in both radial and azimuthal directions; therefore, corneal topography depends not only on the radial direction, but also on the azimuthal direction. This is known as the skew ray error. In this work, we present a numerical analysis on the effects on the corneal topography caused by skew ray error and show the advantages of using illuminated elongated ellipses, which are designed using exact ray tracing, to recover the corneal topography considering a conical corneal topographer.