estuscience - se Eskişehir Technical University Journal of Science and Technology A - Applied Sciences and Engineering 2667-4211 Eskisehir Technical University Algebraic and Differential Geometry Cebirsel ve Diferansiyel Geometri PARABOLAS IN GENERALIZED TAXICAB PLANE PARABOLAS IN GENERALIZED TAXICAB PLANE https://orcid.org/0000-0002-7012-0352 Altıntaş Abdilkadir ESKISEHIR OSMANGAZI UNIVERSITY https://orcid.org/0000-0003-2820-2096 Ekmekçi Süheyla ESKİŞEHİR OSMANGAZİ ÜNİVERSİTESİ 03 27 2026 27 1 99 110 08 14 2025 03 06 2026 Copyright © 2000, Eskişehir Technical University Journal of Science and Technology A - Applied Sciences and Engineering 2000 Eskişehir Technical University Journal of Science and Technology A - Applied Sciences and Engineering

This study investigates parabolas in the generalized taxicab plane, a non-Euclidean geometry where distance is measured using weighted coordinate axes with positive parameters (a,b). Using the focus-directrix definition, it examines the structures of generalized taxicab parabolas (briefly, GTPs) with respect to the positions of their directrices. It is determined that generalized taxicab parabolas are simple rectilinear figures. It further provides a detailed analysis of GTPs, including their axes, vertices, latus rectum, and focal lengths. It reveals that the latus rectum length of a GTP is four times its focal length regardless of the directrix type. Also, the algorithm is presented to visualize GTPs for all types of directrices. Additionally, the study identifies degenerate cases in which the focus is on the directrix, and it is demonstrated that the obtained geometric structures reduce to single lines or unions of planar regions defined by vertical and horizontal lines through the focus.

This study investigates parabolas in the generalized taxicab plane, a non-Euclidean geometry where distance is measured using weighted coordinate axes with positive parameters (a,b). Using the focus-directrix definition, it examines the structures of generalized taxicab parabolas (briefly, GTPs) with respect to the positions of their directrices. It is determined that generalized taxicab parabolas are simple rectilinear figures. It further provides a detailed analysis of GTPs, including their axes, vertices, latus rectum, and focal lengths. It reveals that the latus rectum length of a GTP is four times its focal length regardless of the directrix type. Also, the algorithm is presented to visualize GTPs for all types of directrices. Additionally, the study identifies degenerate cases in which the focus is on the directrix, and it is demonstrated that the obtained geometric structures reduce to single lines or unions of planar regions defined by vertical and horizontal lines through the focus.

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