Analytical Geometry

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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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.

Table of Contents

  • 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


Product details

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

About the Author

Barry Spain

About the Editors

W. J. Langford

E. A. Maxwell

I. N. Sneddon

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