# Analytical Geometry

### The Commonwealth and International Library of Science, Technology, Engineering and Liberal Studies: Mathematics Division

1st Edition - January 1, 1963

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• Author: Barry Spain
• eBook ISBN: 9781483180571

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## Description

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.

• I Introduction

1. Coordinates

2. Distance Between Two Points

3. Ratio

4. Ratio-Formula

5. Area of a Triangle

6. Locus

II Straight Line

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

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

## Product details

• No. of pages: 154
• Language: English
• Published: January 1, 1963
• Imprint: Pergamon
• eBook ISBN: 9781483180571