Coordinate Geometry of Two Dimensions (Hardcover)  | Released: 2006

The present book Coordinate Geometry of Two Dimensions aims at providing the students with a detailed study of Polar Coordinates, Polar Equations of a Straight Line and a Circle, Polar Equations of Conics, General Equation of Second Degree and System of Conics�� the topics included in the UGC syllabus.
Primarily meant for students of B.Sc./B.A. of several Indian Universities, the book exactly covers the prescribed syllabus. It neither includes the irrelevant nor escapes the essential topics. Its approach is explanatory, lucid and comprehensive. The analytic explanation of the subject matter is very systematic which would enable the students to assess and thereby solve the related problems easily. Sufficient number of high-graded solved examples provided in the book facilitate better understanding of the various skills necessary in solving the problems. In addition, practice exercises of multiple varieties will undoubtedly prove helpful in quick revision of the subject. The figures and also the answers provided in the book are accurate and verified thoroughly.
A proper study of the book will definitely bring to students a brilliant success. Even teachers will find it useful in elucidating the subject to the students of Mathematics.Table of Contents: 1. Polar Coordinates, Polar Equations of a Straight Line and a Circle; 1.1. Introduction; 1.2. Polar Coordinates; 1.3. Relation Between Cartesian and Polar Coordinates; 1.4. Distance Between Two Points; 1.5. General Equation of a Line; 1.6. Different Forms of Equation of Straight Line; 1.7. Polar Equation of a Straight Line through Two Given Points; 1.8. Perpendicular Lines; 1.9. Polar Equation of a Circle; 1.10. Equation of the Tangent to the Circle ; 1.11. Area of a Triangle; 2. Polar Equations of Conics; 2.1. Polar Equation of a Conic; 2.2. Axis Inclined at an Angle a; 2.3. Equation to the Directrices; 2.4. Tracing of the Conic; 2.5. Chord Joining Two Points; 2.6. Equation of Tangent; 2.7. Asymptotes; 2.8. Polar; 2.9. Equation of the Normal; 2.10. Pair of Tangents; 3. General Equation of Second Degree; 3.1. Introduction ; 3.2. Definition; 3.3. General Equation of the Conic; 3.4. Particular forms of the Conic; 3.5. General Equation of Second Degree; 3.6. To Show that the General Equation of Second Degree Always Represents a Conic; 3.7. Centre; 3.8. Equation of the Conic Section Referred to the Centre; 3.9. Equation of Asymptotes; 3.10. Nature of the Conic; 3.11. To Find the Lengths and the Positions of the Axes of the Conic; 3.12. Eccentricity, Foci and Directrices; 3.13. Tracing of Conics; 3.14. Tracing of the Parabola; 3.15. The Focus S and Equations of the Directrix and the Latus-rectum; 4. System of Conics; 4.1. Conic through Five Points; 4.2. Conic through Four Points and Touching a Straight Line; 4.3. To Find the General Equation of the Conic Passing through the Point of Intersection of a Curve and a Straight Line; 4.4. To Find the Equations to the Conic Sections Passing through the Intersection of a Conic and Two Given Straight Lines; 4.5. Intersection of Two Conics; 4.6. To Find the General Equation of the Conic Passing through the Points of Intersections of Two Conics; 4.7. Some Special Properties of Circles; 4.8. Common Chord of Two Circles; 4.9. To Find the Equation of the Common Chord of Two Circles; 4.10. To Find the Length of the Common Chord of the Two Circles; 4.11. Equation of Common Chord; 4.12. Angle of Intersection of Two Curves; 4.13. Orthogonal Curves; 4.14. Condition of Orthogonality; 4.15. Angle of Intersection of Two Circles; 4.16. Radical Axis; 4.17. To find the equation of the Radical Axis of the Circles; 4.18. Radical Axis and Common Chord of the Two Circles; 4.19. Circles Intersecting Two Given Circles Orthogonally; 4.20. To Prove that the Radical Axis of Three Circles, Taken Two at a Time, Meet in a Point Provided the Centres, of the Circles Not Collinear; 4.21. Radical Centre; 4.22. To Prove the Circle having Centre at the Radical Centre and Radius Equal to the Length of the Tangent from it to any Circle will Cut all the Three Circles Orthogonally; 4.23. Confocal Conics; 4.24. Confocals through a Given Point; 4.25. Confocals Cut at Right Angles; 4.26. Only One Member of the System of Confocals will Touch a Given Line