Book description
Designed to meet the requirements of undergraduate students, Analytical Geometry: 2D and 3D deals with the theoretical as well as the practical aspects of the subject. Equal emphasis has been given to both 2D as well as 3D geometry. The book follows a systematic approach with adequate examples for better understanding of the concepts.
Table of contents
 Cover
 Title Page
 Brief Content
 Contents
 About the Author
 Dedication
 Preface
 Chapter 1: Coordinate Geometry

Chapter 2: The Straight Line
 2.1 Introduction
 2.2 Slope of a Straight Line
 2.3 Slopeintercept Form of a Straight Line
 2.4 Intercept Form
 2.5 Slopepoint Form
 2.6 Two Points Form
 2.7 Normal Form
 2.8 Parametric Form and Distance Form
 2.9 Perpendicular Distance on a Straight Line
 2.10 Intersection of Two Straight Lines
 2.11 Concurrent Straight Lines
 2.12 Angle between Two Straight Lines
 2.13 Equations of Bisectors of the Angle between Two Lines
 Illustrative Examples
 Exercises

Chapter 3: Pair of Straight Lines
 3.1 Introduction
 3.2 Homogeneous Equation of Second Degree in x and y
 3.3 Angle between the Lines Represented by ax2 + 2hxy + by2 = 0
 3.4 Equation for the Bisector of the Angles between the Lines Given by ax2 + 2hxy + by2 = 0
 3.5 Condition for General Equation of a Second Degree Equation to Represent a Pair of Straight Lines
 Illustrative Examples
 Exercises

Chapter 4: Circle
 4.1 Introduction
 4.2 Equation of a Circle whose Centre is (h, k) and Radius r
 4.3 Centre and Radius of a Circle Represented by the Equation x2 + y2 + 2gx + 2fy + c = 0
 4.4 Length of Tangent from Point P(x1, y1) to the Circle x2 + y2 + 2gx + 2fy + c = 0
 4.5 Equation of Tangent at (x1, y1) to the Circle x2 + y2 + 2gx + 2fy + c = 0
 4.6 Equation of Circle with the Line Joining Points A (x1, y1) and B (x2, y2) as the ends of Diameter
 4.7 Condition for the Straight Line y = mx + c to be a Tangent to the Circle x2 + y2 = a2
 4.8 Equation of the Chord of Contact of Tangents from (x1, y1) to the Circle x2 + y2 + 2gx + 2fy + c = 0
 4.9 Two Tangents can Always be Drawn from a Given Point to a Circle and the Locus of the Point of Intersection of Perpendicular Tangents is a Circle
 4.10 Pole and Polar
 4.11 Conjugate Lines
 4.12 Equation of a Chord of Circle x2 + y2 + 2gx + 2fy + c = 0 in Terms of its Middle Point
 4.13 Combined Equation of a Pair of Tangents from (x1, y1) to the Circle x2 + y2 + 2gx + 2fy + c = 0
 4.14 Parametric Form of a Circle
 Illustrative Examples
 Exercises
 Chapter 5: System of Circles

Chapter 6: Parabola
 6.1 Introduction
 6.2 General Equation of a Conic
 6.3 Equation of a Parabola
 6.4 Length of Latus Rectum
 6.5 Different Forms of Parabola
 Illustrative Examples Based on Focus Directrix Property
 6.6 Condition for Tangency
 6.7 Number of Tangents
 6.8 Perpendicular Tangents
 6.9 Equation of Tangent
 6.10 Equation of Normal
 6.11 Equation of Chord of Contact
 6.12 Polar of a Point
 6.13 Conjugate Lines
 6.14 Pair of Tangents
 6.15 Chord Interms of Midpoint
 6.16 Parametric Representation
 6.17 Chord Joining Two Points
 6.18 Equations of Tangent and Normal
 6.19 Point of Intersection of Tangents
 6.20 Point of Intersection of Normals
 6.21 Number of Normals from a Point
 6.22 Intersection of a Parabola and a Circle
 Illustrative Examples Based on Tangents and Normals
 Illustrative Examples Based on Parameters
 Exercises

Chapter 7: Ellipse
 7.1 Standard Equation
 7.2 Standard Equation of an Ellipse
 7.3 Focal Distance
 7.4 Position of a Point
 7.5 Auxiliary Circle
 Illustrative Examples Based on Focusdirectrix Property
 7.6 Condition for Tangency
 7.7 Director Circle of an Ellipse
 7.8 Equation of the Tangent
 7.9 Equation of Tangent and Normal
 7.10 Equation to the Chord of Contact
 7.11 Equation of the Polar
 7.12 Condition for Conjugate Lines
 Illustrative Examples Based on Tangents, Normals, Polepolar and Chord
 7.13 Eccentric Angle
 7.14 Equation of the Chord Joining the Points
 7.15 Equation of Tangent at ‘θ’ on the Ellipse
 7.16 Conormal Points
 7.17 Concyclic Points
 7.18 Equation of a Chord in Terms of its Middle Point
 7.19 Combined Equation of Pair of Tangents
 7.20 Conjugate Diameters
 7.21 Equiconjugate Diameters
 Illustrative Examples Based on Conjugate Diameters
 Exercises
 Chapter 8: Hyperbola
 Chapter 9: Polar Coordinates

Chapter 10: Tracing of Curves
 10.1 General Equation of the Second Degree and Tracing of a Conic
 10.2 Shift of Origin without Changing the Direction of Axes
 10.3 Rotation of Axes without Changing the Origin
 10.4 Removal of XYterm
 10.5 Invariants
 10.6 Conditions for the General Equation of the Second Degree to Represent a Conic
 10.7 Centre of the Conic Given by the General Equation of the Second Degree
 10.8 Equation of the Conic Referred to the Centre as Origin
 10.9 Length and Position of the Axes of the Central Conic whose Equation is ax2 + 2hxy + by2 = 1
 10.10 Axis and Vertex of the Parabola whose Equation is ax2 + 2hxy + by2 + 2gx + 2fy + c = 0
 Exercises
 Chapter 11: Three Dimension

Chapter 12: Plane
 12.1 Introduction
 12.2 General Equation of a Plane
 12.3 General Equation of a Plane Passing Through a Given Point
 12.4 Equation of a Plane in Intercept Form
 12.5 Equation of a Plane in Normal Form
 12.6 Angle between Two Planes
 12.7 Perpendicular Distance from a Point on a Plane
 12.8 Plane Passing Through Three Given Points
 12.9 To Find the Ratio in which the Plane Joining the Points (x1, y1, z1) and (x2, y2, z2) is Divided by the Plane ax + by + cz + d = 0.
 12.10 Plane Passing Through the Intersection of Two Given Planes
 12.11 Equation of the Planes which Bisect the Angle between Two Given Planes
 12.12 Condition for the Homogenous Equation of the Second Degree to Represent a Pair of Planes
 Illustrative Examples
 Exercises

Chapter 13: Straight Line
 13.1 Introduction
 13.2 Equation of a Straight Line in Symmetrical Form
 13.3 Equations of a Straight Line Passing Through the Two Given Points
 13.4 Equations of a Straight Line Determined by a Pair of Planes in Symmetrical Form
 13.5 Angle between a Plane and a Line
 13.6 Condition for a Line to be Parallel to a Plane
 13.7 Conditions for a Line to Lie on a Plane
 13.8 To Find the Length of the Perpendicular from a Given Point on a Line
 13.9 Coplanar Lines
 13.10 Skew Lines
 13.11 Equations of Two Nonintersecting Lines
 13.12 Intersection of Three Planes
 13.13 Conditions for Three Given Planes to Form a Triangular Prism
 Illustrative Examples
 Illustrative Examples (Coplanar Lines and Shortest Distance)
 Exercises

Chapter 14: Sphere
 14.1 Definition of Sphere
 14.2 The equation of a sphere with centre at (a, b, c) and radius r
 14.3 Equation of the Sphere on the Line Joining the Points (x1, y1, z1) and (x2, y2, z2) as Diameter
 14.4 Length of the Tangent from P(x1, y1, z1) to the Sphere x2 + y2 + z2 + 2ux + 2vy + 2wz + d = 0
 14.5 Equation of the Tangent Plane at (x1, y1, z1) to the Sphere x2 + y2 + z2 + 2ux + 2vy + 2wz + d = 0
 14.6 Section of a Sphere by a Plane
 14.7 Equation of a Circle
 14.8 Intersection of Two Spheres
 14.9 Equation of a Sphere Passing Through a Given Circle
 14.10 Condition for Orthogonality of Two Spheres
 14.11 Radical Plane
 14.12 Coaxal System
 Illustrative Examples
 Exercises

Chapter 15: Cone
 15.1 Definition of Cone
 15.2 Equation of a Cone with a Given Vertex and a Given Guiding Curve
 15.3 Equation of a Cone with its Vertex at the Origin
 15.4 Condition for the General Equation of the Second Degree to Represent a Cone
 15.5 Right Circular Cone
 15.6 Tangent Plane
 15.7 Reciprocal Cone
 Exercises
 Chapter 16: Cylinder
 Acknowledgement
 Copyright
 Back Cover
Product information
 Title: Analytical Geometry
 Author(s):
 Release date: May 2013
 Publisher(s): Pearson India
 ISBN: 9789332517646
You might also like
book
Introduction to Abstract Algebra, 4th Edition
Praise for the Third Edition ". . . an expository masterpiece of the highest didactic value …
book
Geometry Essentials For Dummies
Geometry Essentials For Dummies (9781119590446) was previously published as Geometry Essentials For Dummies (9781118068755). While this …
book
Classical Geometry: Euclidean, Transformational, Inversive, and Projective
Features the classical themes of geometry with plentiful applications in mathematics, education, engineering, and science Accessible …
book
Tiny Python Projects
The projects are tiny, but the rewards are big: each chapter in Tiny Python Projects challenges …