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Analytical Geometry
The Commonwealth and International Library of Science, Technology, Engineering and Liberal Studies: Mathematics Division
- 1st Edition - January 1, 1963
- Author: Barry Spain
- Editors: W. J. Langford, E. A. Maxwell, I. N. Sneddon
- Language: English
- eBook ISBN:9 7 8 - 1 - 4 8 3 1 - 8 0 5 7 - 1
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… Read more
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Request a sales quoteAnalytical 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.
I Introduction
1. Coordinates
2. Distance Between Two Points
3. Ratio
4. Ratio-Formula
5. Area of a Triangle
6. Locus
II Straight Line
7. Gradient
8. Equation of a Straight Line
9. Linear Equation
10. Equation of the Straight Line Through Two Points
11. Intercept Form
12. Normal Form
13. Angle Between Two Straight Lines
14. Intersection of Two Straight Lines
15. Concurrency
16. Sign of the Expression u Ξ ax + by + c
17. Perpendicular Distance of a Point from a Straight Line
18. Bisectors of Angles Between two Straight Lines
19. Pencil of Straight Lines
20. Parametric Equations of a Straight Line
III Straight Line
21. Homogeneous Equation of the Second Degree
22. Condition that S Ξ ax2+2hxy+by2+2gx+2fy+c = 0 Represents Two Straight Lines
23. Angle Between the Line-Pair S = 0
24. Bisectors of the Line-Pair ax2+2hxy+by2 = 0
25. Equation of Lines Joining the Origin to the Points of Intersection of S Ξ ax2+2hxy+by2+2gx+2fy+c = 0 and the Straight Line u Ξ lx+my+n = 0
IV Circle
26. Equation of a Circle
27. Length of the Tangent from a Point to a Circle
28. Circle with Given Diameter
29. Intersection of x2+y2 = r2 and y = mx+c
30. Joachimsthal's Equation
31. Tangent to a Circle
32. Condition that a Line be Tangent to a Circle
33. Chord Joining Points of Contact of Tangents from a Point
34. Pair of Tangents from a Point to a Circle
35. Parametric Treatment of the Circle
V Systems of Circle
36. Angle of Intersection of Two Circles
37. Radical Axis
38. Radical Centre
39. Coaxal Circles
40. Intersecting Coaxal Circles
41. Non-Intersecting Coaxal Circles
42. Conjugate System of Coaxal Circles
VI Ellipse
43. Ellipse
44. Intersection of x2—a2 + y2-b2 = 1 and y = mx+c
45. Tangent Properties
46. Parametric Equations
47. Conjugate Diameters
48. Normal
49. Geometrical Properties
VII Hyperbola
50. Hyperbola
51. Tangent Properties
52. Parametric Equations
53. Asymptotes
54. Conjugate Diameters
55. Normal
56. Geometrical Properties
VIII Rectangular Hyperbola
57. Rectangular Hyperbola
58. Parametric Equations of Rectangular Hyperbola
59. Chord and Tangent
60. Chord of Contact
61. Conjugate Diameters
62. Normals
63. Concyclic Points
64. Tangent Properties
IX Parabola
65. Parabola
66. Parametric Equations
67. Chord and Tangent
68. Chord of Contact
69. Diameters
70. Normals
71. Concyclic Points
72. Geometrical Properties
73. Tangent Properties
Answers
- No. of pages: 154
- Language: English
- Edition: 1
- Published: January 1, 1963
- Imprint: Pergamon
- eBook ISBN: 9781483180571
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