Coordinate Geometry for JEE (Advanced), 3rd edition 9353503795, 9789353503796

Citation preview

Contents

Preface 1.

Coordinate System

1.31

Linked Comprehension Type Matrix Match Type Numerical Value Type

1.1-1.34

1.31 1.32

Introduction Rectangular (or Cartesian) Coordinate System

1.1

Archives

1.33

1.1

Answers Key

1.33

Transformation of Axes Concept Application Exercise 1.1

1.2

Distance Formula and Area of Polygon Distance Formula

1.4

1.4

2.

2.1-2.42

Straight Lines

2.1

Equation of Line in Different Forms

1.4

Equation of Line in Point-Slope Form

Polygon

1.6

Equation of Line Passing Through Two Points

Concept Application Exercise 1.2

1.8

(Two Points Form)

2.3

Equation of Line in Intercept Form

2.5

Equation of Line in Normal Form

2.7

Area of a

Section Formula Internal Division External Division Coordinates of Different Centres of Triangle Centroid Circumcentre Orthocentre

1.9 1.9 1.9 1.10

1.10 1.11 1.12

Incentre

1.13

Excentres of Triangle

1.14

Slope of a Line

Concept Application Exercise 1.3 Slope of Line Joining Given Two Points Slope of Line Having Given Equation Angle between Two Lines

1.15

2.1

Concept Application Exercise 2.1

2.8

Equation of Straight Line in Symmetric form (Parametric or Distance form)

2.9

Concept Application Exercise 2.2

2.11

Distance of a Point from a Line

2.11

Concept Application Exercise 2.3

2.14

Position of a Point w.r.t. a Line

2.15

Division of Plane by Line

2.17

1.15

1.16 1.16 1.17

Concept Application Exrercise 2.4

2.19

Image of a Point in a Line and Equation of Angle Bisectors

2.19

Concept Application Exercise 1.4

1.19

Polar Coordinates Coordinate Conversion

1.19

Foot of Perpendicular Drawn from a Point a Line and Image of Point in a Line

1.20

Equations of Bisectors of the Angles between

Concept Application Exercise 1.5

1.21

Locus and its Equation Finding Equation of Locus by Elimination of Given Variable

1.21

Concept Application Exercise 1.6

1.23

Solved Examples

1.24

Exercises Single Correct Answer Iype

1.27

Multiple Correct Answers Type

1.23

1.27 1.30

the Lines

Bisector

on

2.19 2.21

Containing

the Given Point

Concept Application Exercise 2.5 Concurrency of Three Lines and Family of Straight Lines

Concurrency of Three Lines Family of Lines

Concept Application Exercise 2.6 Solved Examples

2.21

2.24 2.24 2.24

2.25 2.2

2.2

iv

Contents

Exercises Single Correct Answer Type Multiple Correct Answers Type Linked Comprehension Type Matrix Match Type

Numerical V'alue Type Archives Answers Ker 3.

Pair of Straight Lines

Lines Equation of Pair of Straight Second the Degree in General Equation of Two Variables

Concept Application Exercise 3.1 Second-Degree Homogeneous Equation Angle between Pair of Straight Lines Equation of Pair of Angle Bisectors of Given

2.32

Intersection of Line and Circle

2.36 2.38 2.39 2.40

Length of Tangent

to Circle

Secant of Circle

Equation of Chord of Circle Bisected at Given Point

2.41

Concept Application Exercise

2.42

Tangent and Normal to Circle Equation of Tangent to Circle at a Given Point

3.1-3.10

4.3

4.13 4.14 4.15 4.16 4.18 4.18

on the Circle

4.19 4.19

3.1

Equation of Tangent to Circle Having Given Slope 4.20

3.1

Equation of Tangents to Circle Drawn from External Point

3.2

Equation of Pair of Tangents

3.3 3.4

Chord of Contact Director Circle

4.21 4.22 4.23 4.23

Normal to Circle

4.24

3.4

Concept Application Exercise 4.4

4.25

Homogenization of Second Degree Equation

3.5

4.25

Concept Application Exercise 3.2

3.5

Sohved Examples

3.6

Different Cases of Two Circles Radical Axis of Two Circles Radical Axes of Three Circles Taken Two at a

Exercises Multiple Correct Answers Type

3.8 3.8 3.9

Linked Comprehension Type

3.9

Pair of Straight Lines

Single Correct Answer Type

Numerical Value Type Answers Key

4.

Maximum and Minimum Distance of a Point from the Circle

2.32

Circle Definition Equation of Circle in Centre-Radius Form

Time and Radical Centre Two Disjoint Circles

4.26 4.27

3.10

3.10

without Touching

4.32

Family of Circles

435

4.1

Concept Application Exercise 4.6

4.35

4.1

Solved Examples

4.35

Exercises Single Correct Answer Type Multiple Correct Answers Type

4.40 4.40

General Form of Equation of Circle

4.5

Equation of Circle Passing through Three Points

4.7

Concept Application Exercise 4.1

4.8

Linked Comprehension Type Matrix Match Type

Some More Forms of Equation of Circle

4.8

Numerical Value Type

Equation of Circle Circumscribing Triangle and Quadrilateral

4.46 447

4.50 451 4.5

Archives

4.53

Answers Key 4.8 5.

4.9 4.10

5.1-548

Parabola

5.1 5.1

Conic Section: Introduction

Conic Section as Locus of a Point

5.2

Standard Equation of Parabola 4.11

Equation of Chord

of Parabola Bisected at

Concept Application Exercise 4.2

4.12

Given Point

Geometry with Circle

4.12

Position ofa Point with Respect to

4.12

Parametric Form of Parabola

Position of Point w.r.t. Circle

4.29

4.33

4.4

Equation of Circle in Parametric Form

4.28

Concept Application Exercise 4.5 4.1-4.54

Equation of Circle Touching One or Both the

Equation of Circle Having Given End Points of Diameter

4.26

Two Circles Touching Externally Two Circles Touching Internally Two Intersecting Circles One Circle Contained in the Other Circle

Coordinate Axes

Equation of Circle Having Given End Points of Chord which Subtends Given Angle at the Circumference

4.25

a

Parabola

5. 5.5

5.5

Concept Application Exercise Other Forms of Parabola

Contents V 5.1

Equation of Parabola Having Axis Parallel to x-Axis Equation of Parabola Having Axis Parallel to y-Axis of

Equation

Equation of Chord of Ellipse Bisected at

5.6

Given Point

5.7

5.7 5.7

Parametric Form of Ellipse Some Important Properties of Ellipse

Parabola with Given Focus

and Directrix

5.10

Concept Application Exercise 5.2

5.12

Focal Chord and its

Concept Application

5.12

Tangent to Ellipse A Line and an Ellipse

Properties

Concept Application Evercise 5.3

5.14

Tangent to Parabola

5.14

Intersection of a Line and a Parabola Equation of Tangent to Standard Parabola

5.14

Equation of Tangent to any Parabola

5.17

Equation of Pair of Tangents

5.18

Equation of Chord of Contact

5.19 5.20

Properties of Tangent

5.20

6.10 6.13 6.14

Exercise 6.3

6.14 6.14

6.14 Equation of Tangent to Ellipse Having Given Slope 6.15

of Tangent to Ellipse at a Given 6.16 Point on it Equation of Tangent to Ellipse from External Point 6.18

Equation

5.14

Concept Application Exercise 5.4

6.9

Equation of Chord of Ellipse

Equation of Pair of Tangents from External Point

6.18

Director Circle

6.19

Chord of Contact

6.19

Properties of Tangent

6.21

Concept Application Exercise 6.4

Locus of Point of Intersection of Tangent

6.23 6.23

Normal to Ellipse

under Different Conditions

5.22

Concept 4pplication Exercise 5.5

5.23

Equation of Normal to Point on it

Normal to Parabola

5.23

Equation of Normal to Ellipse with Given Slope

6.24

5.25

Important Property of Normal

Concept Application Exercise 5.6

5.27

Conormal Points

6.25 6.26

Properties of Normal

5.27

Concept Application Exercise 6.5

5.29

Solved Examples

6.26 6.27

Concept Application Exercise 5.7

5.31

Exercises

6.30

Solved Examples

5.31

Single Correct Answer Type

6.30

Exercises

S.37

Multiple Correct Answers Type

6.33

Linked Comprehension Type

6.34

Matrix Match Type Numerical Value Type

6.37

Normal to Parabola from a Point not Lying on it

Conormal Point and its Properties

6.

6.9

Concept Application Exercise 6.2

Ellipse

at

a

Given

6.23

Single Correct Answer Type

5.37

Multiple Correct Answers Type

Linked Comprehension Type Matrix Match Type

5.41 5.43 5.44

Archives

6.37

Numerical Value Type

5.45

Answers Key

6.40

Archives

5.45

Answers key

5.47 6.1-6.40

Ellipse

7.

36

7.1-7.42

Hyperbola

Definition

7.1

Concept Application Exercise 7.1 Equation of Hyperbola and Its Properties Standard Equation of Hyperbola

Definition

6.1

Concept Application Exercise 6.1

6.3

Equation of Ellipse in Different Forms

6.3

Equation of Hyperbola Referred to

6.3

Two Perpendicular Lines as Axes

7.9

Division of Plane

7.9

Standard Equation of Ellipse

Equation

of Ellipse

Having

Axes Parallel to

Coordinate Axes

Equation of an Ellipse Referred Area of Ellipse Position of a Point w.r.t. Ellipse

Important Property of Focal Chord

by Hyperbola

6.6

Important Property of Focal Chord Equation of Chord of Hyperbola Bisected

6.7 6.7

at Given Point

7.10

Parametric Form of Hyperbola Important Property of Auxiliary Circle Equation of Chord of Hyperbola

7.11

to Two

Perpendicular Lines as Axes

7.3

Hyperbola Having Axes Parallel to Coordinate Axes 7.7

6.8 6.8

7.10

7.11 7.12

vi

Contents

Concept Application Exrercise

7.2

Tangent to Hyperbola A Line and a Hyperbola Equation of Tangent to Hyperbola Having Given Slope of Tangent to

Hyperbola at a

Point

Equation Tangents to Hyperbola from a Point not Lying on it and Chord of Contact

it

on

7.13

Concept Application Exercise

7.13

Solved Examples

7.13

Exercises Single Correct Answer Type

7.14 7.15

7.16 7.17 7.18

Concept Application Exercise 7.3

7.18

Asymptotes of Hyperbola (Tangent at Infinity)

.19

Properties of Asymptotes 7.4

Normal to Hyperbola

Equation of Normal to Hyperbola at a

Point

Multiple Correct Answers Type

Linked Comprehension Type Matrix Match Type

Director Circle Properties of Tangent to Hyperbola

Concept 4pplication Exercise

7.6

on

it

Numerical Value Type

7.28 1.28 7.32 7.32 7.36 7.37 7.38 7.39

Archives

7.40

Answers Key

7.42

Solutions

S.1-S.174

7.20

Chapter

7.21

Chapter 2

S.19

7.22

Chapter 3

S.47

7.22

Chapter 4

S.53

Chapter 5

S.89

Equation of Normal to Hyperbola Having

S.I

Given Slope

7.22

Chapter 6

S.124

Important Property of Normal

7.24

Chapter 7

S.152

Concept Application Exercise 7.5

7.25 7.25

Hyperbola Having Asymptotes as Coordinate Axes

Tangent and Normal to Hyperbola

7.26

Appendix Chapterwise Solved January 2019 JEE Main

Questions (AJI Sets)

A.1-A.4