On looking for a simplified method for dealing with the paraxial lens formulas one finds that by using the lens focal length F as a unit of measure the paraxial equations quickly simplify to a pair of graphs readily depicting the locus of all possible object and image parameters (location and size) for converging lenses (lenses with thick centers). A "thin lens" is converging if its center is thicker than its edges. A "thick" converging lens has object and image distances measured from principle planes rather than lens center as in a "thin" lens.
"Dimensional Analysis Of The Paraxial Equations Of Optics", Proc. SPIE 0190, Los Alamos Conference on Optics 1979, (13 November 1980); doi: 10.1117/12.957717; https://doi.org/10.1117/12.957717