Spain / Langford / Maxwell Analytical Geometry

The Commonwealth and International Library of Science, Technology, Engineering and Liberal Studies: Mathematics Division
1. Auflage 2014
ISBN: 978-1-4831-8057-1
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 154 Seiten, Web PDF

Analytical Geometry contains various topics in analytical geometry, which are required for the advanced and scholarship levels in mathematics of the various Examining Boards. This book is organized into nine chapters and begins with an examination of the coordinates, distance, ratio, area of a triangle, and the concept of a locus. These topics are followed by discussions of the straight line, straight lines, circle, systems of circles, ellipse, hyperbola, rectangular hyperbola and parabola. This work provides exercises for each section and each chapter ends with a miscellaneous set of examples. Answers are supplied at the end of the book. This book will prove useful to advanced analytical geometry students.

Autoren/Hrsg.

Spain, Barry

Langford, W. J.

Maxwell, E. A.

Sneddon, I. N.

Inhaltsverzeichnis

1;Front Cover;1
2;Analytical Geometry;4
3;Copyright Page;5
4;Table of Contents;6
5;Preface;10
6;CHAPTER 1. Introduction;14
6.1;1. Coordinates;14
6.2;2. Distance between two points;16
6.3;3. Ratio;17
6.4;4. Ratio-formula;18
6.5;5. Area of a triangle;20
6.6;6. Locus;24
6.7;MISCELLANEOUS EXAMPLES;25
7;CHAPTER II. Straight Line;26
7.1;7. Gradient;26
7.2;8. Equation of a straight line;27
7.3;9. Linear equation;29
7.4;10. Equation of the straight line through two points;30
7.5;11. Intercept form;32
7.6;12. Normal form;32
7.7;13. Angle between two straight lines;34
7.8;14. Intersection of two straight lines;37
7.9;15. Concurrency;38
7.10;16. Sign of the expression u = ax+by+c;39
7.11;17. Perpendicular distance of a point from a straight line;40
7.12;18. Bisectors of angles between two straight lines;42
7.13;19. Pencil of straight lines;44
7.14;20. Parametric equations of a straight line;46
7.15;MISCELLANEOUS EXAMPLES;48
8;CHAPTER III. Straight Lines;51
8.1;21. Homogeneous equation of the second degree;51
8.2;22. Condition that S=ax2+2hxy+by2+2gx+2fy+c=0 represents two straight lines;52
8.3;23. Angle between the line-pair S = 0;54
8.4;24. Bisectors of the line-pair ax2+2hxy+by2 = 0;55
8.5;25. Equation of lines joining the origin to the points of inter-section of S = ax2+2hxy+by2+2gx+2fy+c = 0 and the straight line u = lx+my+n = 0;56
8.6;MISCELLANEOUS EXAMPLES;58
9;CHAPTER IV. Circle;59
9.1;26. Equation of a circle;59
9.2;27. Length of the tangent from a point to a circle;61
9.3;28. Circle with given diameter;63
9.4;29. Intersection of x2+y2 = r2 and y = mx+c;64
9.5;30. Joachimsthal's equation;65
9.6;31. Tangent to a circle;67
9.7;32. Condition that a line be tangent to a circle;69
9.8;33. Chord joining points of contact of tangents from a point;70
9.9;34. Pair of tangents from a point to a circle;72
9.10;35. Parametric treatment of the circle;74
9.11;MISCELLANEOUS EXAMPLES;76
10;CHAPTER V. Systems of Circles;78
10.1;36. Angle of intersection of two circles;78
10.2;37. Radical axis;80
10.3;38. Radical centre;81
10.4;39. Coaxal circles;82
10.5;40. Intersecting coaxal circles;84
10.6;41. Non-intersecting coaxal circles;85
10.7;42. Conjugate system of coaxal circles;86
10.8;MISCELLANEOUS EXAMPLES;87
11;CHAPTER VI. Ellipse;88
11.1;43. Ellipse;88
11.2;44. Intersection of x2a2+y2b2 = 1 and y=mx+c;90
11.3;45. Tangent properties;93
11.4;46. Parametric equations;95
11.5;47. Conjugate diameters;97
11.6;48. Normal;100
11.7;49. Geometrical properties;101
11.8;MISCELLANEOUS EXAMPLES;103
12;CHAPTER VII. Hyperbola;105
12.1;50. Hyperbola;105
12.2;51. Tangent properties;108
12.3;52. Parametric equations;109
12.4;53. Asymptotes;111
12.5;54. Conjugate diameters;113
12.6;55. Normal;114
12.7;56. Geometrical properties;115
12.8;MISCELLANEOUS EXAMPLES;116
13;CHAPTER VIII. Rectangular Hyperbola;118
13.1;57. Rectangular hyperbola;118
13.2;58. Parametric equations of rectangular hyperbola;121
13.3;59. Chord and tangent;123
13.4;60. Chord of contact;126
13.5;61. Conjugate diameters;128
13.6;62. Normals;129
13.7;63. Concyclic points;131
13.8;64. Tangent properties;132
13.9;MISCELLANEOUS EXAMPLES;134
14;CHAPTER IX. Parabola;136
14.1;65. Parabola;136
14.2;66. Parametric equations;137
14.3;67. Chord and tangent;139
14.4;68. Chord of contact;141
14.5;69. Diameters;142
14.6;70. Normals;143
14.7;71. Concyclic points;144
14.8;72. Geometrical properties;145
14.9;73. Tangent properties;147
14.10;MISCELLANEOUS EXAMPLES;149
15;Answers;151