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Master's Dissertation
DOI
10.11606/D.55.2018.tde-01022018-141551
Document
Author
Full name
Regina Lourenço de Barros
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 2017
Supervisor
Committee
Ribeiro, Hermano de Souza (President)
Capelato, Érika
Rodrigues, Hildebrando Munhoz
Simal, Janete Crema
Title in Portuguese
Cônicas
Keywords in Portuguese
Cônicas
Função quadrática
Geometria analítica
Abstract in Portuguese
Este trabalho trata das seções cônicas (circunferência, elipse, hipérbole e parábola), curvas planas obtidas pela intersecção de um cone circular reto com um plano. O objetivo do trabalho é representar algebricamente essas figuras geométricas. As referidas curvas serão estudadas num sistema cartesiano ortogonal. Nos primeiros capítulos as cônicas serão estudadas individualmente com relação aos seus elementos e às equações que descrevem cada curva. Serão apresentadas as equações canônicas, as equações paramétricas e as equações em coordenadas polares dentre outras. Destaque especial é dado às retas tangentes a essas curvas. No último capítulo as cônicas serão relacionadas através da equação geral. Serão estudados métodos que permitem a identificação e caracterização dessas curvas a partir da equação geral.
Title in English
Conics
Keywords in English
Analitic geometry
Conics
Quadratic function
Abstract in English
This paper deals with the conic sections (circumference, ellipse, hyperbola and parabola), plane curves obtained by the intersection of a right circular cone with a plane. The objective of this work is to represent these geometric figures algebraically. These curves will be studied in an orthogonal Cartesian system. In the first chapters the conics will be studied individually with respect to their elements and to the equations that describe each curve. The canonical equations, the parametric equations and the equations in polar coordinates, among others, will be presented. Special emphasis is given to the tangent lines to these curves. In the last chapter the conics will be related through the general equation. Methods will be studied that allow the identification and characterization of these curves from the general equation.
 
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Publishing Date
2018-02-01
 
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