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Coordinate
Geometry Booster
with Problems & Solutions
for
JEE
Main and Advanced
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About the Author
REJAUL MAKSHUD (RM)
Post Graduated from Calcutta University in PURE MATHEMATICS.
Presently, he trains IIT Aspirants at RACE IIT Academy, Jamshedpur.
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Coordinate
Geometry Booster
with Problems & Solutions
for
JEE
Main and Advanced
Rejaul Makshud
M. Sc. (Calcutta University, Kolkata)
McGraw Hill Education (India) Private Limited
CHENNAI
McGraw Hill Education Offices
Chennai NewYork St Louis SanFrancisco Auckland Bogotá Caracas
Kuala Lumpur Lisbon London Madrid Mexico City Milan Montreal
San Juan Santiago Singapore Sydney Tokyo Toronto
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McGraw Hill Education (India) Private Limited
Published by McGraw Hill Education (India) Private Limited
444/1, Sri Ekambara Naicker Industrial Estate, Alapakkam, Porur, Chennai - 600 116
Coordinate Geometry Booster
Copyright © 2017, McGraw Hill Education (India) Private Limited.
No part of this publication may be reproduced or distributed in any form or by any means, electronic, mechanical,
photocopying, recording, or otherwise or stored in a database or retrieval system without the prior written permission
of the publishers. The program listings (if any) may be entered, stored and executed in a computer system, but they
may not be reproduced for publication.
This edition can be exported from India only by the publishers,
McGraw Hill Education (India) Private Limited
ISBN (13): 978-93-5260-509-5
ISBN (10): 93-5260-509-8
Information contained in this work has been obtained by McGraw Hill Education (India), from sources believed to be
reliable. However, neither McGraw Hill Education (India) nor its authors guarantee the accuracy or completeness
of any information published herein, and neither McGraw Hill Education (India) nor its authors shall be responsible
for any errors, omissions, or damages arising out of use of this information. This work is published with the
understanding that McGraw Hill Education (India) and its authors are supplying information but are not attempting
to render engineering or other professional services. If such services are required, the assistance of an appropriate
professional should be sought.
Typeset at The Composers, 260, C.A. Apt., Paschim Vihar, New Delhi 110 063 and text and cover printed at
Cover Designer: Creative Designer
visit us at: www.mheducation.co.in
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Dedicated to
My Parents
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Preface
COORDINATE GEOMETRY BOOSTER with Problems & Solutions for JEE Main and Advanced is meant for aspirants
preparing for the entrance examination of different technical institutions, especially NIT/IIT/BITSAT/IISc. In writing this
book, I have drawn heavily from my long teaching experience at National Level Institutes. After many years of teaching, I have
realised the need of designing a book that will help the readers to build their base, improve their level of mathematical concepts
and enjoy the subject.
This book is designed keeping in view the new pattern of questions asked in JEE Main and Advanced Exams. It has six
chapters. Each chapter has the concept booster followed by a large number of exercises with the exact solutions to the problems
as given below:
Level - I : Problems based on Fundamentals
Level - II : Mixed Problems (Objective Type Questions)
Level - III : Problems for JEE Advanced Exam
Level - IV : Tougher Problems for JEE-Advanced Exam
(0.......9) : Integer Type Questions
Passages : Comprehensive Link Passages
Matching : Matrix Match
Previous years’ papers : Questions asked in previous years’ JEE-Advanced Exams
Remember friends, no problem in mathematics is difficult. Once you understand the concept, they will become easy. So
please don’t jump to exercise problems before you go through the Concept Booster and the objectives. Once you are confident
in the theory part, attempt the exercises. The exercise problems are arranged in a manner that they gradually require advanced
thinking.
I hope this book will help you to build your base, enjoy the subject and improve your confidence to tackle any type of
problem easily and skilfully.
My special thanks goes to Mr. M.P. Singh (IISc. Bangalore), Mr. Manoj Kumar (IIT, Delhi), Mr. Nazre Hussain (B. Tech.),
Dr. Syed Kashan Ali (MBBS) and Mr. Shahid Iqbal, who have helped, inspired and motivated me to accomplish this task. As
a matter of fact, teaching being the best learning process, I must thank all my students who inspired me most for writing this
book.
I would like to convey my affectionate thanks to my wife, who helped me immensely and my children who bore with
patience my neglect during the period I remained devoted to this book.
I also convey my sincere thanks to Mr Biswajit Das of McGraw Hill Education for publishing this book in such a beautiful
format.
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viii Preface
I owe a special debt of gratitude to my father and elder brother, who taught me the first lessons of Mathematics and to all my
learned teachers— Mr. Swapan Halder, Mr. Jadunandan Mishra, Mr. Mahadev Roy and Mr. Dilip Bhattacharya, who instilled
the value of quality teaching in me.
I have tried my best to keep this book error-free. I shall be grateful to the readers for their constructive suggestions toward
the improvement of the book.
Rejaul Makshud
M. Sc. (Calcutta University, Kolkata)
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Contents
Preface vii
Chapter 1 Straight Lines 1.1–1.74
Rectangular Cartesian Co-ordinates 1.1
Introduction 1.1
Co-ordinate Axes and Rectangular Axes 1.1
Cartesian Co-ordinates 1.1
Polar Co-ordinates 1.1
Relation between the Cartesian and Polar Co-ordinates 1.1
Distance between two Points (Cartesian Form) 1.2
Section Formulae 1.2
Area of a Triangle 1.4
Locus and its Equation 1.4
Geometrical Transformations 1.5
Rotation of Co-ordinate Axes 1.5
Straight Line 1.6
Introduction 1.6
Definitions 1.6
Angle of Inclination of a Line 1.6
Forms of a Straight Line 1.7
Reduction of General Equation into Standard Form 1.8
Position of Two Points with Respect to a Given Line 1.8
Equation of a Line Parallel to a Given Line 1.8
Equation of a Line Perpendicular to a Given Line 1.8
Distance from a Point to a Line 1.8
Point of Intersection of two Lines 1.9
Equation of Straight Lines Passing through a Given Point and Making a
Given Angle with a Given Line 1.10
A Line is Equally Inclined with Two Lines 1.10
Equation of Bisectors 1.10
Foot of the Perpendicular Drawn From the Point (x,y) to the Line ax + by + c = 0 1.10
1 1
Image of a Point (x,y) with Respect to a Line Mirror ax + by + c = 0 1.10
1 1
Reflection of Light 1.11
Exercises 1.12
Answers 1.28
Hints and Solutions 1.31
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