Conics Inscribed in a Standard Triangle in the Isotropic Plane

In this paper, we study conics inscribed in a standard triangle in the isotropic plane. Our research gives the conditions under which the inscribed conic is an ellipse, a parabola, or a hyperbola, expressed through the elements of a standard triangle. We also determine and analyze the loci of centers of certain conics, leading to the discovery of interesting new and previously unknown results on inscribed conics of a standard triangle in the isotropic plane. We further explore the analogies between these findings and those in the Euclidean plane.