The paper presents the outcomes of a long-term individual educational trajectory for a team of secondary school students. The topic isoptic of a curve with asymptotes appears naturally when two viewpoints on isoptic are compared. The result about hyperbola hints that the curve with asymptote needs special attention when considering the locus of visibility, but not just the locus of points from which the tangents meet at a constant angle. The particular cases for the exponent and logarithm are studied. The proofs are based on calculations by a computer algebra system (CAS), and the illustrations are done by a dynamic geometry system (DGS).