Work

Scrutinizing the General Conic Equation

Year: 2025

Type: article

Abstract: We present a general formula that transforms any conic of the form Ax2+Bxy+Cy2+Dx+Ey+F=0, with B≠0, into A′(x′)2+C′(y′)2+D′x′+E′y′+F=0, without requiring the rotation angle θ. This directly eliminates the cross term xy, simplifying the rotated conics analysis. As consequences, we obtain new formulae that remove both rotations and translations, a novel proof of the discriminant criterion, improved expressions for eccentricity, and a detailed taxonomy of all loci described by the general conic equation.

Source: Mathematics

DOI: 10.3390/math13091428

Authors: Mauricio Chávez-Pichardo, José Daniel López-Barrientos, Saúl Perea-Flores

Institutions: Tecnológico Nacional de México, Tecnológico de Estudios Superiores del Oriente del Estado de México, Universidad Anáhuac, PNC Financial Services (United States)

Language: English

Topic: Mathematics and Applications

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $3,137

OpenAlex ID: W4409896607

FWCI:

Cites: 3

Cited by:

Related to: 10