Analytic Geometry

This respected text makes extensive use of applications and features items such as historical vignettes to make the material useful and interesting. The text is written for the one-term analytic geometry course, often taught in sequence with college algebra, and is designed for students with a reasonably sound background in algebra, geometry, and trigonometry.

Preface

v

Inroduction to the Graphing Calculator

ix

Plane Analytic Geometry

1

(50)

The Cartesian Plane

1

(2)

Distance Formula

3

(8)

Point-of-Division Formulas

11

(9)

Inclination and Slope

20

(5)

Parallel and Perpendicular Lines

25

(5)

Angle from One Line to Another

30

(6)

Graphs and Points of Intersection

36

(9)

An Equation of a Locus

45

(6)

Vectors in the Plane

51

(34)

Directed Line Segments and Vectors

51

(10)

The Dot Product

61

(9)

Applications of Vectors

70

(15)

The Line

85

(41)

Point-Slope and Two-Point Forms

85

(11)

Slope-Intercept and Intercept Forms

96

(10)

Distance from a Point to a Line

106

(9)

Families of Lines

115

(11)

The Circle

126

(23)

The Standard Form for an Equation of a Circle

126

(12)

Conditions to Determine a Circle

138

(11)

Conic Sections

149

(37)

Inroduction

149

(1)

The Parabola

149

(12)

The Ellipse

161

(12)

The Hyperbola

173

(13)

Transformation of Coordinates

186

(37)

Translation of Conic Sections

186

(14)

Translation of General Equations

200

(6)

Rotation

206

(5)

The General Equation of Second Degree

211

(12)

Curve Sketching

223

(58)

Symmetry and Intercepts

223

(11)

Sketching Polynomial Equations

234

(13)

Asymptotes

247

(9)

Sketching Rational Functions

256

(9)

Radicals and the Domain of the Equation

265

(9)

Direct Sketching of Conics

274

(7)

Polar Coordinates and Parametric Equations

281

(35)

Polar Coordinates

281

(1)

Graphs in Polar Coordinates

282

(8)

Points of Intersection

290

(4)

Relationships between Rectangular and Polar Coordinates

294

(5)

Conics in Polar Coordinates

299

(6)

Parametric Equations

305

(11)

Solid Analytic Geometry

316

(88)

Inroduction: The Distance and Point-of-Division Formulas

316

(6)

Vectors in Space

322

(6)

Direction Angles, Cosines, and Numbers

328

(6)

The Line

334

(8)

The Cross Product

342

(9)

The Plane

351

(10)

Cylinders and Spheres

361

(4)

Quadric Surfaces

365

(13)

Cylindrical and Spherical Coordinates

378

(9)

APPENDICES

A Trigonometry Review

387

(8)

B Formulas

395

(4)

C Theorems from Plane Geometry

399

(5)

Answers to Odd-Numbered Problems

404

(65)

Index

469

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Table of Contents

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