  In this paper we study a general class of conics starting from a quotient
field. We give a group structure over these conics generalizing the
construction of a group over the Pell hyperbola. Furthermore, we generalize the
definition of R\'edei rational functions in order to use them for evaluating
powers of points over these conics. Finally, we study rational approximations
of irrational numbers over conics, obtaining a new result for the approximation
of quadratic irrationalities.
