Analytical Geometry

Two Dimensions

Sibdas Karmakar, Samiran Karmakar

• Editorial: CRC Press
• Año: 2022
• ISBN:
  9781000593471
• Edición: 1
• Categoría: Matemáticas
• Categoría: Geometría analítica

This book is a compilation of all basic topics of Analytical Geometry of Two Dimensions and is intended to serve as an introductory text aimed towards undergraduate and graduate students in science and technology. An understanding of basic school level algebra and geometry can serve as the prerequisite for following this book. The present work is no original work but an attempt to make the subject thoroughly intelligible. All the important properties of the conics have been discussed either in the articles or in illustrative examples. Each chapter has sufficient completely solved problems and a set of carefully graded and motivating unsolved exercises.

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Chapter 1 Transformation of Rectangular Cartesian Coordinates

1.1 Introduction

In analytical geometry the position of a point is determined with the help of a coordinate system, for which we require an arbitrarily chosen origin and two straight lines intersecting at the origin. This follows that the coordinates of a point are different for different sets of axes. That is the coordinates of a point are relative. This may happen when the origin is shifted to a point keeping the directions of the axes unchanged or when the axes are rotated through an angle keeping the origin unaltered. The former is called translation and the later is called rotation. The coordinates of any point may also be affected by a combination of these two, called a rigid motion or orthogonal transformation.

In this chapter, we shall establish formulas corresponding to the above transformations.

1.2 Coordinate Transformation Formulas

1.2.1 Translation (or transformation by translation of axes)

If the origin be shifted to any other point without changing the directions of coordinate axes, the result is known ...