There are various ways of building mirror lens systems to focus light, parabolic mirrors, hyperbolic mirrors, spherical mirrors etc.
Each has trade-offs - such as costs to manufacture, and benefits - optical performance - lack of coma.
The RC is a particularly good but hard to manufacture, costly design. See here:
http://www.rcopticalsystems.com/
esigned principally as a photographic instrument by American George Ritchey and Frenchman Henri Chrétien, the Ritchey-Chrétien optical design is coma free. Coma is an aberration common in all reflecting telescope systems. The Ritchey-Chrétien design utilizes a hyperbolic primary mirror and secondary mirror. This design corrects for coma and results in a smaller spot size on and off axis
http://www.atscope.com.au/rcos.html
Meade Instruments has recently announced an "Advanced Ritchie Chrétien design" telescope. Sadly their advertising hyperbolae is very misleading about type of optical design these telescopes employ. They are clearly not Ritchie Chrétien's. The Ritchie Chrétien design ( inverted in 1910s by George Willis Ritchey and Henri Chrétien, their design is used in many, if not most of the largest professional astronomical telescopes ) uses two hyperbolic mirrors only. The Meade RCX design is a clear step ahead of the standard schmidt cassegrain telescope, however, any design that uses a correcting plate is a Catadioptric. As a consequence, their design has off-axis chromatic aberrations which are shown "spot diagrams" below. The polychromatic spot size matrix shown here clearly shows the chromatic error introduced by the addition of a corrector plate. The design employed in the Meade RCX has been well known to optical designers for over a decade, and is more correctly called an aplanatic schmidt cassegrain design. The design is not without merit. Though the spot sizes are significantly larger than a classical Ritchie Chretien, the off-axis performance is superior to a standard Schmidt Cassegrain.