Chapter 2

प्रस्तावना

This section introduces the book 'Co-ordinate Geometry and Mathematical Programming Problems' designed according to the curriculum of Vardhman Mahaveer Open University, Kota, for B.Sc. Part I Mathematics, Paper III. The language of the book is intentionally kept simple, engaging, and easy to grasp. The nature of mathematics is considered, and appropriate use of English terminology is made alongside Hindi explanations. The section highlights that various units are written by expert authors, who have referred to standard texts to ensure factual accuracy. The book aims to guide students for competitive exams as well. The preface expresses gratitude to the contributors and assures students that the book will be helpful for both academic and competitive purposes.

• Book is designed for B.Sc. Part I Mathematics, Paper III.
• Language is simple, engaging, and easy to understand.
• English terminology is used alongside Hindi explanations.
• Units are written by subject experts using standard references.
• Book is useful for competitive exams.
• 📌 Co-ordinate Geometry: The branch of mathematics dealing with geometric figures using coordinates.
• 📌 Mathematical Programming: The study of mathematical techniques for optimization problems.

इकाई 1 : X-Y में व्यापक द्विघाती कार्तीय समीकरण का उनके मानक रूप में समानयन (Reduction of general equation of second degree Cartesian equation in X-Y to their standard forms)

This section outlines the structure of Unit 1, which focuses on reducing the general second-degree Cartesian equation in X-Y to its standard forms. The unit covers objectives, introduction, definitions (including conic section, mathematical definition, focus, directrix, eccentricity), transformation of axes by rotation, general equation of conic section, theorems, special cases, center of conic section, absence of coefficients of x and y, coordinates of the center, conditions for conic section, summary, terminology, answers to self-assessment questions, and practice questions. The main objective is to learn how to reduce the general quadratic equation to standard forms such as straight lines, points, parabola, hyperbola, and to determine the center of these conic sections.

• Unit focuses on reducing general second-degree equations to standard forms.
• Includes definitions, transformation of axes, and special cases.
• Covers finding the center of conic sections.
• Provides conditions for conic sections and practice questions.
• 📌 Conic Section: A curve obtained by intersecting a cone with a plane.
• 📌 Standard Form: The simplified form of an equation representing a geometric figure.
• 📌 Center: The point equidistant from all points on the conic section.