We prove (under some technical assumptions) that each surface in R3 containing two arcs of parabolas with axes parallel to Oz through point has a parametrization (P(u,v)R(u,v),Q(u,v)R(u,v),Z(u,v)R2(u,v)) for P,Q,R,Z∈R[u,v] such P,Q,R have degree at most 1 u and v, Z 2 v. The proof is based on the observation one can consider parabola vertical axis as an isotropic circle; this allows us use meth...