# Analytic Geometry

## 1st Edition

Authors:
eBook ISBN: 9781483262413
Published Date: 1st January 1971
Page Count: 240
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## Description

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.

﻿Preface

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

6-5 Applications

6-6 The Ellipse

6-7 Applications

6-8 The Hyperbola

6-9 General Definition of the Conic Sections

7. The General Second-Degree Equation

7-1 Introduction

7-2 The Reduction of (7-1) to the Form (5-1)

7-3 Invariants and Identification

8. Parametric Equations

8-1 Some Basic Concepts

8-2 Parametric Representation-Introduction

8-3 Parametric Representation-Some Examples

9. Polar Coordinates

9-1 Introduction

9-2 Definitions

9-3 Sketching Polar Curves

9-4 Intersection of Polar Curves

9-5 Polar Equations of the Conics

10. Rectangular Coordinates in Three Dimensions

10-1 The Coordinate System

10-2 The Distance Formula

10-3 Planes Parallel to the Coordinate Planes

10-4 Directions on a Line

11. Surfaces and Curves

11-1 Introduction

11-2 Traces and Sections

11-3 Intercepts and Symmetry

11-4 Sketching Surfaces

11-5 Cylindrical Surfaces

11-6 Projections of Curves on the Coordinate Planes

11-7 Surfaces of Revolution

11-8 Cylindrical Coordinates

11-9 Spherical Coordinates

12. Lines and Planes

12-1 Parametric Equations of a Line

12-2 Symmetric Equations of a Line

12-3 The Plane

12-4 Distance from a Point to a Plane

12-5 More about Lines

Answers to Odd-Numbered Exercises

Index

Table of Trigonometric Functions

No. of pages:
240
Language:
English