Conceptual Geometry of Straight Line


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Conceptual Geometry of Straight Line

A Companion to S. L. Loney's Co-ordinate Geometry

About the Book

This work contains conceptual solutions to the problems and exercises given in Chapters I-VI (Covering Straight Line) of S. L. Loney's Co-ordinate Geometry including variations of problems, solutions, methods and approaches.

These solutions strengthen and enliven the inherent multi-concepts to enrich the heritage set forth by S. L. Loney.

The present work will serve as a complete guide to private students reading the subject with few or no opportunities of instruction. This will save the time and lighten the work of Teachers as well.

This book helps in acquiring a better understanding of the basic principles of Straight Line (Co-ordinate Geometry) and in revising a large amount of the subject matter quickly. Care has been taken, as in the forthcoming ones, to present the solutions with multi-concepts and beyond in a simple natural manner, in order to meet the difficulties which are most likely to arise, and to render the work intelligible and instructive.

About the Author

Chandra Shekhar Kumar
Chandra Shekhar Kumar

Chandra Shekhar Kumar is Staff Software Architect @ GE Healthcare (Ultrasound Digital Solutions). In an innovator role, he is actively involved in digital Innovation in Ultrasound ecosystem (premise, edge and cloud) including (but not limited to) C++17/20/23, Boost C++ Libraries, WineLib, Qt, wxWidgets, WebAssembly,, Hashicorp Nomad and Rust. Motto is to build once and run everywhere using the same code base (using and extending WebAssembly Infrastructure)

He is Co-Founder of Ancient Science Publishers (estd.2014), a venture to publish monographs on mathematics, physics and computer science and render services related to hiring technical talents, training for competitive programming, algorithms, programming interviews, IITJEE and Olympiads. Inspiration for this undertaking came from the writings of Leonhard Euler (mathematics), Richard Phillips Feynman (physics) and Edsger Wybe Dijkstra (computer science).

He is Founder of Ancient Kriya Yoga Mission (estd.2013), a venture to disseminate simple techniques of ancient science of living and publish kriya yoga scriptures and commentaries.

He holds a degree of Integrated M.Sc.(5 yrs) in Physics from IIT Kanpur.

He has worked with software companies like Trilogy, Oracle and few start-ups.

He has been programming in C++ for the last 22 years. He loves to hack gcc, gdb, valgrind, clang, boost, TeX, LaTeX and pours inside the works of Dijkstra and Knuth.

Table of Contents

1 Introduction

1.1 Algebraic Results . . . . . . . . . . . . . . . . . . . . . .

2 Coordinates : Lengths of Straight Lines and Areas of Triangles

2.1 Coordinates . . . . . . . . . . . .

2.2 Length of Straight Line . . . . .

2.3 Areas of Triangles . . . . . . . .

2.4 Polar Coordinates . . . . . . . . .

3 Locus : Equation to a Locus

4 Straight Line : Rectangular Coordinates

4.1 Equations, Slope and Intercepts . . . . . . .

4.2 Angles between straight lines . . . . . . . . .

4.3 Lengths of Perpendiculars . . . . . . . . . . .

4.4 Bisectors of angles between straight lines .

5 The Straight Line : Polar Equations, Oblique Coordinates and Loci

5.1 Oblique Coordinates . . . . . . . . . . . . . . . . . . . .

5.2 Straight lines passing through xed pts. . . . . . . . .

5.3 Loci . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

6 On Equations Representing Two Or More Straight

6.1 Multiple Straight Lines and Included Angles . . .

6.2 General Equation of The Second Degree . . . . .

6.3 Equations Representing Isolated Points .

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