Analytic Geometry

419 Pages·1982·20.833 MB·English

by  Douglas F. Riddle

ANALYTIC GEOMETRY
Douglas F. Riddle / Third Edition

ANALYTIC
GEOMETRY

ANALYTIC GEOMETRY
THIRD EDITION
DOUGLAS F. RIDDLE
St. Joseph’s University
Wadsworth Publishing Company
Belmont, California
A Division of Wadsworth, Inc.
ISBN 0-S3M-Q103Q-X
Mathematics Editor: Richard Jones
Production: Greg Hubit Bookworks
Cover art: Circular Forms (1912) by Robert Delaunay. © A.D.A.G.P.
© 1982 by Wadsworth, Inc.
© 1977, 1972 by Wadsworth Publishing Company, Inc. All rights
reserved. No part of this book may be reproduced, stored in a
retrieval system, or transcribed, in any form or by any means,
electronic, mechanical, photocopying, recording, or otherwise,
without the prior written permission of the publisher, Wadsworth
Publishing Company, Belmont, California 94002, a division of
Wadsworth, Inc.
Printed in the United States of America
3 4 5 6 7 8 9 10—86 85 84 83
Library of Congress Cataloging in Publication Data
Riddle, Douglas F.
Analytic geometry.
First-2nd eds. published as: Analytic geometry with vectors.
Includes index.
1. Geometry, Analytic. I. Title.
QA551.R48 1982 516.3 81-14695
ISBN 0-5 34-01030-X AACR2
CONTENTS
PREFACE ix
1
PLANE ANALYTIC GEOMETRY 1
1.1 The Cartesian Plane 1
1.2 Distance Formula 4
1.3 Point-of-Division Formulas 10
1.4 Inclination and Slope 16
1.5 Parallel and Perpendicular Lines 21
1.6 Angle from One Line to Another 24
1.7 Graphs and Points of Intersection 30
1.8 An Equation of a Locus 33
2
VECTORS IN THE PLANE 38
2.1 Directed Line Segments and Vectors 38
2.2 The Dot Product 48
2.3 Applications of Vectors 55
v
vi Contents
3
THE LINE 62
3.1 Point-Slope and Two-Point Forms 62
3.2 Slope-Intercept and Intercept Forms 68
3.3 Distance from a Point to a Line 74
3.4 Families of Lines 81
3.5 Fitting a Line to Empirical Data 88
4
THE CIRCLE 95
4.1 The Standard Form for an Equation of a Circle 95
4.2 Conditions to Determine a Circle 101
4.3 Families of Circles 108
5
CONIC SECTIONS 115
5.1 Introduction 115
5.2 The Parabola 115
5.3 The Ellipse 123
5.4 The Hyperbola 131
5.5 Reflection Properties of Conics 138
5.6 Conics and a Right Circular Cone 147
6
TRANSFORMATION OF COORDINATES 152
6.1 Translation of Conic Sections 152
Contents vii
6.2 Translation of General Equations 163
6.3 Rotation 168
6.4 The General Equation of Second Degree 173
7
CURVE SKETCHING 181
7.1 Intercepts and Asymptotes 181
7.2 Symmetry, Sketching 190
7.3 Radicals and the Domain of the Equation 198
7.4 Direct Sketching of Conics 203
8
TRANSCENDENTAL CURVES 208
8.1 Trigonometric Functions 208
8.2 Inverse Trigonometric Functions 212
8.3 Exponential and Logarithmic Functions 216
8.4 Hyperbolic Functions 220
9
POLAR COORDINATES AND PARAMETRIC EQUATIONS 224
9.1 Polar Coordinates 224
9.2 Graphs in Polar Coordinates 226
9.3 Points of Intersection 232
9.4 Relationships between Rectangular and Polar Coordinates 235
9.5 Conics in Polar Coordinates 239
9.6 Parametric Equations 245
9.7 Parametric Equations of a Locus 252