Analytical Geometry, 1/e : 2D and 3D.

Format:

Book

Author/Creator:

Vittal, P. R.

Language:

English

Subjects (All):

Geometry, Analytic--Problems, exercises, etc.

Geometry, Analytic.

Physical Description:

1 online resource (753 pages)

Edition:

1st ed.

Other Title:

Analytical Geometry, 1/e

Place of Publication:

Delhi : Pearson India, 2013.

Summary:

PMP® Certification: Excel with Ease is a self-study guide and is essential to all PMP aspirants to clear the certification exam in the first attempt itself. The book is based on A Guide to the Project Management Body of Knowledge (PMBOK® Guide), fifth edition, which presents a set of standard terminology and guidelines for project management. The content presented in an easy to understand format which shall help students to grasp concepts quickly.

Contents:

Cover

Dedication

Brief Contents

Contents

About the Author

Preface

Chapter 1: Coordinate Geometry

1.1 Introduction

1.1.1 Distance between Two Given Points

1.2 Section Formula

1.2.1 Coordinates of the Point that Divides the Line Joining Two Given Points in a Given Ratio

1.2.2 External Point of Division

1.2.3 Centroid of a Triangle Given its Vertices

1.2.4 Area of Triangle ABC with Vertices A(x1, y1), B(x2, y2) and C(x3, y3)

1.2.5 Area of the Quadrilateral Given its Vertices

Illustrative Examples

Exercises

Chapter 2: The Straight Line

2.1 Introduction

2.1.1 Determination of the General Equation of a Straight Line

2.1.2 Equation of a Straight Line Parallel to y-axis and at a Distance of h units from x-axis

2.2 Slope of a Straight Line

2.3 Slope-intercept Form of a Straight Line

2.4 Intercept Form

2.5 Slope-point 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

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 ax 2 + 2hxy + by 2 = 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

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

4.10.1 Polar of the Point P (x1, y1) with Respect to the Circle x2 + y2 + 2gx + 2fy + c = 0

4.10.2 Pole of the Line lx + my + n = 0 with Respect to the Circle x2 + y2 = a2

4.11 Conjugate Lines

4.11.1 Condition for the Lines lx + my + n = 0 and l1x + m1y + n1 = 0 to be Conjugate Lines with Respect to the Circle x2 + y2 = a2

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

4.14.1 Equation of the Chord Joining the Points 'θ' and 'ᵩ' on the Circle and the Equation of the Tangent at θ

Chapter 5: System of Circles

5.1 Radical Axis of Two Circles

5.2 Orthogonal Circles

5.3 Coaxal System

5.4 Limiting Points

5.5 Examples (Radical Axis)

5.6 Examples (Limiting Points)

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

6.4.1 Tracing of the curve y2 = 4ax

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 Mid-point

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

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 Focus-directrix 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, Pole-polar 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

7.20.1 Locus of Midpoint

7.20.2 Property: The Eccentric Angles of the Extremities of a Pair of Semi-conjugate Diameter Differ by a Right Angle

7.20.3 Property: If CP and CD are a Pair of Semi-conjugate Diameters then CD2 + CP2 is a Constant.

7.20.4 Property: The Tangents at the Extremities of a Pair of Conjugate Diameters of an Ellipse Encloses a Parallelogram Whose Area Is Constant

7.20.5 Property: The Product of the Focal Distances of a Point on an Ellipse Is Equal to the Square of the Semi-diameter Which Is Conjugate to the Diameter Through the Point

7.20.6 Property: If PCP ' and DCD ' are Conjugate Diameter then They are also Conjugate Lines

7.21 Equi-conjugate Diameters

7.21.1 Property: Equi-conjugate Diameters of an Ellipse Lie along the Diagonals of the Rectangle Formed by the Tangent at the Ends of its Axes

Illustrative Examples Based on Conjugate Diameters

Chapter 8: Hyperbola

8.1 Definition

8.2 Standard Equation

8.3 Important Property of Hyperbola

8.4 Equation of Hyperbola in Parametric Form

8.5 Rectangular Hyperbola

8.6 Conjugate Hyperbola

8.7 Asymptotes

8.7.1 Equations of Asymptotes of the Hyperbola

8.7.2 Angle between the Asymptotes

8.8 Conjugate Diameters

8.9 Rectangular Hyperbola

8.9.1 Equation of Rectangular Hyperbola with Reference to Asymptotes as Axes

8.9.2 Equations of Tangent and Normal at (x1, y1) on the Rectangular Hyperbola xy = c2

8.9.3 Equation of Tangent and Normal at (ct,c/t)on the Rectangular Hyperbola xy = c2

8.9.4 Equation of the Chord Joining the Points 't1' and 't2' on the Rectangular Hyperbola xy = c2 and the Equation of the Tangent at t

8.9.5 Properties

8.9.6 Results Concerning the Rectangular Hyperbola

8.9.7 Conormal Points-Four Normal from a Point to a Rectangular Hyperbola

8.9.8 Concyclic Points on the Rectangular Hyperbola

Chapter 9: Polar Coordinates

9.1 Introduction

9.2 Definition of Polar Coordinates

9.3 Relation between Cartesian Coordinates and Polar Coordinates

9.4 Polar Equation of a Straight Line.

9.5 Polar Equation of a Straight Line in Normal Form

9.6 Circle

9.6.1 Polar Equation of a Circle

9.6.2 Equation of the Chord of the Circle r = 2a cos θ on the Line Joining the Points (r1, θ1) and (r2, θ2).

9.6.3 Equation of the Normal at α on the Circle r = 2cosθ

9.6.4 Equation of the Circle on the Line Joining the Points (a, α) and (b, β) as the Ends of a Diameter

9.7 Polar Equation of a Conic

9.7.1 Polar Equation of a Conic

9.7.2 Equation to the Directrix Corresponding to the Pole

9.7.3 Equation to the Directrix Corresponding to Focus Other than the Pole

9.7.4 Equation of Chord Joining the Points whose Vectorial Angles are ` - a and ` + a on the Conic

9.7.5 Tangent at the Point whose Vectorial Angle is ` on the Coniclr=1+ ecosp

9.7.6 Equation of Normal at the Point whose Vectorial Angle is a on the Conic

9.7.7 Asymptotes of the Conic islr=1+ecosp (e>1)

9.7.8 Equation of Chord of Contact of Tangents from (r1,p1) to the Conic

9.7.9 Equation of the Polar of any Point (r1,p1) with Respect to the Coniclr=1+ ecosp

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 XY-term

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

Chapter 11: Three Dimension

11.1 Rectangular Coordinate Axes.

11.2 Formula for Distance between Two Points.

Notes:

Description based on publisher supplied metadata and other sources.

Includes index.

ISBN:

93-325-1763-0

OCLC:

1024243802