The definition of a conchoid surface is:
rc[u, v] = r[u, v] + k (r[u, v] - P)/Norm[r[u, v] - P] and rc[u, v] = r[u, v] - k (r[u, v] - P)/Norm[r[u, v] - P], P is the pole, k distance and r[u, v] the base surface.In this notebook we will obtain the conchoid surface of the sphere {Cos[u]Cos[v] + 1.25, Sin[u]Cos[v], Sin[v]} with the distance k = 1.5 and as pole P the origin.