Palindromic pairs in conics

Abstract

For each point p? ([0 , 1] n Q) 2 we define and classify a family (C(p; k)) k ? Z of rational conics passing through p, each one containing a sequence of rational points (xnk,ynk)n=-k converging to p and such that the continued fraction of xnk and ynk are reversal to one another. Moreover the points (xnk,ynk,k)k?Z,n=-k are contained in a quartic surface Q(p) whose intersection with horizontal planes are conics.