Analytic Geometry - 1st Edition - ISBN: 9780121422561, 9781483262413

Analytic Geometry

1st Edition

Authors: A. C. Burdette
eBook ISBN: 9781483262413
Imprint: Academic Press
Published Date: 1st January 1971
Page Count: 240
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Analytic Geometry covers several fundamental aspects of analytic geometry needed for advanced subjects, including calculus.

This book is composed of 12 chapters that review the principles, concepts, and analytic proofs of geometric theorems, families of lines, the normal equation of the line, and related matters. Other chapters highlight the application of graphing, foci, directrices, eccentricity, and conic-related topics. The remaining chapters deal with the concept polar and rectangular coordinates, surfaces and curves, and planes.

This book will prove useful to undergraduate trigonometric students.

Table of Contents


1. The Coordinate System—Fundamental Relations

1-1 Introduction

1-2 Directed Lines

1-3 Cartesian Coordinates

1-4 Projections of a Line Segment on Horizontal and Vertical Lines

1-5 Point of Division on a Line Segment

1-6 Distance between Two Points

1-7 Slope of a Line

1-8 Parallel and Perpendicular Lines

1-9 Angle Formed by Intersecting Lines

1-10 Analytic Proofs of Geometric Theorems

2. The Straight Line

2-1 Equation and Locus

2-2 The Graph of an Equation

2-3 The Graph of a Linear Equation

2-4 The Point-Slope Equation

2-5 The Two-Point Equation

2-6 The Slope-Intercept Equation

2-7 The First-Degree Equation

2-8 Intersection of Lines

2-9 The Normal Equation of the Straight Line

2-10 Distance from a Line to a Point

2-11 Families of Lines

2-12 Families of Lines through the Intersection of Two Lines

3. Graphs of Nonlinear Equations

3-1 Introduction

3-2 Intercepts

3-3 Symmetry

3-4 Extent

3-5 Horizontal and Vertical Asymptotes

3-6 Graphing Equations

4. Transformation of Coordinates

4-1 Introduction

4-2 Translation of Axes

4-3 Rotation of Axes

5. Graphing the Equation Ax2 + By2 + Cx + Dy + E = 0

5-1 Introduction

5-2 Case I: A = B

5-3 Case II: Either A = 0 or B = 0

5-4 Case III: A and B of the Same Sign, A ≠ B

5-5 Case IV: A and B of Different Signs

6. The Conic Sections

6-1 Introduction

6-2 The Circle

6-3 Families of Circles

6-4 The Parabola



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© Academic Press 1971
Academic Press
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About the Author

A. C. Burdette

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