## Description

This textbook is meant for students of first course on Analytical Geometry. The book provides balanced coverage of both theory and practice of concepts. A wide variety of problems and lucid language will help students understand and apply the concepts easily. The step-by-step solutions to solved problems enables clear understanding. A variety of solved and unsolved problems have been incorporated to help student’s ace university and competitive examinations.

## Table of Content

**Chapter 1 Analytical Geometry of Two Dimensions**

1.1 The Parabola

1.1.1 Some Standard Results Related to the Parabola y ^2= 4ax

1.2 The Ellipse

1.2.1 Some Standard Results Related to the Ellipse

(x ^2)/(a ^2 ) + (y ^2)/(b ^2 ) = 1

1.3 The Hyperbola

1.3.1 Some Standard Results Relating to the Hyperbola

(x ^2)/(a ^2 ) − (y ^2)/(b ^2 ) = 1

1.4 Co-normal and Concyclic Points

1.4.1 Co-normal Points on the Parabola y ^2= 4ax

1.4.2 Concyclic Points on the Parabola y ^2= 4ax

1.4.3 Co-normal Points on the Ellipse (x ^2)/(a ^2 ) + (y ^2)/(b ^2 ) = 1

1.4.4 Concyclic Points on the Ellipse (x ^2)/(a ^2 ) + (y ^2)/(b ^2 ) = 1

1.5 Diameter and Conjugate Diameters

1.5.1 Definition and Equation for the Diameter of the Parabola

1.5.2 Diameters of the Ellipse and the Hyperbola

1.6 Asymptotes of the Hyperbola

1.6.1 The Equations of the Asymptotes of the Hyperbola

(x ^2)/(a ^2 ) − (y ^2)/(b ^2 ) = 1

1.7 Conjugate Hyperbola

1.7.1 Equation of Conjugate Hyperbola

1.7.2 The Relation among the forms of the Equations of a

Hyperbola, its Conjugate and Asymptotes

1.7.3 Equation of a Rectangular Hyperbola referred to its

Asymptotes as Co-ordinate Axes

1.7.4 Some of the Standard Results Relating to the R.H. xy = c^2

**Chapter 2 Analytic Geometry of Three Dimensions**

2.1 Introduction – Direction Cosines and the Plane

2.2 Direction Ratios of the Line Joining Two Points

2.3 The Plane

**Chapter 3 Plane and the Straight Line**

3.1 The Straight Line

3.2 The Plane and the Straight Line

3.3 Shortest Distance Between Two Skew Lines

**Chapter 4 Sphere and Circle**

4.1 Definition

4.2 Standard form of the Equation to a Sphere

4.3 Tangent Line and Tangent Plane

**Chapter 5 Cone and Cylinder**

5.1 Cone and Right Circular Cone

5.1.1 Definition

5.1.2 Equation of a Cone with Vertex at the Origin

5.1.3 General Equation of a Right Circular Cone

5.2 Cylinder

5.2.1 Definition

5.3 Right Circular Cylinder

5.3.1 Definition

## About The Author

**T. Veerarajan** is Dean (Retd.), Department of Mathematics, Velammal College of Engineering and Technology, Madurai, Tamil Nadu. A Gold Medalist from Madras University, he has had a brilliant academic career all through. He has 50 years of teaching experience at undergraduate and postgraduate levels in various established engineering colleges in Tamil Nadu including Anna University, Chennai.

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