Analytical Geometry
The Commonwealth and International Library of Science, Technology, Engineering and Liberal Studies: Mathematics Division
Published on 9. May 2014
154 pages
978-1-4831-8057-1 (ISBN)
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.
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Content
I Introduction 1. Coordinates 2. Distance Between Two Points 3. Ratio 4. Ratio-Formula 5. Area of a Triangle 6. LocusII 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 ¿ 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 LineIII Straight Line 21. Homogeneous Equation of the Second Degree 22. Condition that S ¿ 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 ¿ ax2+2hxy+by2+2gx+2fy+c = 0 and the Straight Line u ¿ lx+my+n = 0IV 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 CircleV 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 CirclesVI 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 PropertiesVII Hyperbola 50. Hyperbola 51. Tangent Properties 52. Parametric Equations 53. Asymptotes 54. Conjugate Diameters 55. Normal 56. Geometrical PropertiesVIII 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 PropertiesIX 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 PropertiesAnswers
