Analytic Geometry

by Riddle, Douglas R.

• ISBN13: 9780534948542
• ISBN10: 0534948545
• Edition: 6th
• Format: Hardcover
• Copyright: 1995-10-25
• Publisher: Cengage Learning

Summary

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.

Table of Contents

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