Description
McGraw Hill Coordinate Geometry Booster With Problems & Solutions For Jee Main & Advanced 2Nd Edition by Makshud, Rejaul
Coordinate Geometry Booster for IIT-JEE Main and Advanced has been conceptualised and produced for aspirants of various engineering entrance examinations. It renders complex concepts and problems of Coordinate Geometry easy for the students and provides them as many opportunities for guided practice as needed. It covers all topics, and is imbued with a strong conceptual approach, with relevant theory being followed by plenty of solved exercise questions, graded LODs and past years’ papers. The various levels of difficulties have numerous MCQs, integer type questions, comprehensive link passage questions and matrix match questions for ample practice and thorough understanding. Step-by-step guidance in problem solving and alternative methods of approaching a problem are included to boost aspirants’ analytical and mathematical skills and are intended to teach them independent problem-solving techniques based upon the solutions.
SALIENT FEATURES
• Covers the latest JEE (Main & Advanced) syllabus as per the JEE Pattern
• Exercise questions graded into Level I, Level II, Level III and Level IV
• Level I questions based on Fundamentals
• Level II based on Mixed Problems
• Level III consist of Problems for JEE Advanced
• Level IV comprise of Tougher Problem
• Chapter-wise previous years’ questions with complete solution
• Solutions to questions have been provided in a step-by-step manner and alternate methods of solution have also been used wherever applicable
TABLE OF CONTENTS
Preface vii
1. Chapter 1 Straight Lines 1.1–1.74
2. Rectangular Cartesian Co-ordinates 1.1
3. Introduction 1.1
4. Co-ordinate Axes and Rectangular Axes 1.1
5. Cartesian Co-ordinates 1.1
6. Polar Co-ordinates 1.1
7. Relation between the Cartesian and Polar Co-ordinates 1.1
8. Distance between two Points (Cartesian Form) 1.2
9. Section Formulae 1.2
10. Area of a Triangle 1.4
11. Locus and its Equation 1.4
12. Geometrical Transformations 1.5
13. Rotation of Co-ordinate Axes 1.5
14. Straight Line 1.6
15. Introduction 1.6
16. Definitions 1.6
17. Angle of Inclination of a Line 1.6
18. Forms of a Straight Line 1.7
19. Reduction of General Equation into Standard Form 1.8
20. Position of Two Points with Respect to a Given Line 1.8
21. Equation of a Line Parallel to a Given Line 1.8
22. Equation of a Line Perpendicular to a Given Line 1.8
23. Distance from a Point to a Line 1.8
24. Point of Intersection of two Lines 1.9
25. Equation of Straight Lines Passing through a Given Point and Making a
26. Given Angle with a Given Line 1.10
27. A Line is Equally Inclined with Two Lines 1.10
28. Equation of Bisectors 1.10
29. Foot of the Perpendicular Drawn From the Point (x1, y1) to the Line ax + by + c = 0 1.10
30. Image of a Point (x1, y1) with Respect to a Line Mirror ax + by + c = 0 1.10
31. Reflection of Light 1.11
32. Exercises 1.12
33. Answers 1.28
34. Hints and Solutions 1.31
35. Chapter 2 Pair of Straight Lines 2.1–2.20
36. Introduction 2.1
37. Homogeneous Equation 2.1
38. Pair of Straight Lines through the Origin 2.1
39. Angle Between the Lines Represented by ax2 + 2hxy + by2 = 0 2.2
40. Bisectors of Angles between the Lines Represented by ax2 + 2hxy + by2 = 0 2.2
41. General Equation of 2nd Degree is ax2 + 2hxy + by2 + 2gx + 2fy + c = 0 2.2
42. Exercises 2.3
43. Answers 2.8
44. Hints And Solutions 2.9
45. Chapter 3 Circle 3.1–3.83
46. Introduction 3.1
47. Mathematical Definitions 3.1
48. Standard Equation of a Circle 3.2
49. General Equation of a Circle 3.2
50. Nature of the Circle 3.2
51. Concentric Circles 3.2
52. Concyclic Points 3.2
53. Parametric Equation of a Circle 3.2
54. Diametric form of a Circle 3.3
55. Equation of a Circle Passing through Three Non-collinear Points 3.3
56. Cyclic Quadrilateral 3.3
57. Condition for Concyclic Points 3.3
58. Intercepts Made on the Axes by a Circle 3.3
59. Different Forms of a Circle 3.3
60. Position of a Point with Respect to a Circle 3.4
61. Shortest and Largest Distance of a Circle from a Point 3.4
62. Intersection of a Line and a Circle 3.4
63. Length of Intercept Cut off from a Line by a Circle 3.5
64. Tangent and Secant 3.5
65. Director Circle 3.7
66. Normal 3.7
67. Chord of Contact 3.8
68. Chord Bisected at a Given Point 3.8
69. Diameter of a Circle 3.8
70. Pole and Polar 3.9
71. Common Chord of Two Circles 3.9
72. Intersection between Two Circles 3.9
73. Angle of Intersection of Two Circles 3.11
74. Radical Axis 3.11
75. Properties of the Radical Axis 3.11
76. Radical Centre 3.13
77. Family of Circles 3.13
78. Exercises 3.14
79. Answers 3.35
80. Hints and Solutions 3.37
81. Chapter 4 Parabola 4.1–4.63
82. Introduction 4.1
83. Basic definitions 4.1
84. Conic Section 4.2
85. Recognition of Conics 4.2
86. Equation of Conic Section 4.2
87. Parabola 4.3
88. Mathematical Definitions 4.3
89. Standard Equation of a Parabola 4.3
90. Important Terms Related to Parabola 4.4
91. General Equation of a Parabola 4.5
92. Equation of a Parabola When the Vertex is (h, k) and Axis is Parallel to x-axis 4.5
93. Equation of a Parabola when the Vertex is (h, k) and Axis is Parallel to y-axis 4.5
94. Focal Chord 4.5
95. Position of a Point Relative to a Parabola 4.6
96. Intersection of a Line and a Parabola 4.6
97. Tangent 4.6
98. Normal 4.7
99. Chord of Contact 4.8
100. Chord Bisected at a Given Point 4.8
101. Diameter 4.8
102. Reflection Property of a Parabola 4.9
103. Exercises 4.9
104. Answers 4.21
105. Hints and Solutions 4.23
106. Chapter 5 Ellipse 5.1–5.68
107. Introduction 5.1
108. Mathematical Definitions 5.1
109. Equation of an Ellipse 5.2
110. Properties of an Ellipse 5.2
111. Parametric Equation of an Ellipse 5.3
112. Important Properties Related to Chord and Focal Chord 5.4
113. Position of a Point with Respect to an Ellipse 5.5
114. Intersection of a Line and an Ellipse 5.6
115. The Length of the Chord Intercepted by the Ellipse on the Line y = mx + c. 5.6
116. Various Forms of Tangents 5.6
117. Director Circle 5.6
118. Pair of Tangents 5.6
119. Various Forms of Normals 5.7
120. Number of Normals are Drawn to an Ellipse From a Point to its Plane 5.7
121. Chord of Contact 5.8
122. Chord Bisected at a Given Point 5.8
123. Pole and Polar 5.8
124. Diameter 5.8
125. Conjugate Diameters 5.8
126. Reflection Property of an Ellipse 5.10
127. Exercises 5.10
128. Answers 5.24
129. Hints and Solutions 5.27
130. Chapter 6 Hyperbola 6.1–6.59
131. Introduction 6.1
132. Mathematical Definitions 6.1
133. Standard Equation of a Hyperbola 6.2
134. Definition and basic terminology of the hyperbola
135. Position of a Point with Respect to a Hyperbola 6.5
136. Intersection of a Line and a Hyperbola 6.5
137. Different Forms of Tangents 6.6
138. Different Forms of Normals 6.7
139. Chord of Contact 6.7
140. Equation of the Chord Bisected at a Point 6.7
141. Pole and Polar 6.7
142. Diameter 6.8
143. Conjugate Diameters 6.8
144. Asymptotes 6.8
145. Rectangular Hyperbola 6.9
146. Rectangular Hyperbola
147. Reflection Property of a Hyperbola 6.10
148. Exercises 6.10
149. Answers 6.23
150. Hints and Solutions 6.24