एक पृथ्वी अतिपरवलय की जनक रेखाएँ

प्रस्तावना

The preface introduces the book 'Co-ordinate Geometry and Mathematical Programming Problems', created as per the curriculum of Vardhman Mahaveer Open University, Kota for B.Sc. Part I Mathematics, Paper III. The language of the book is designed to be simple, engaging, and easy to comprehend. Considering the nature of mathematics, appropriate use of English terminology is made alongside Hindi. Various units are authored by subject experts, who have referred to standard texts to ensure factual accuracy. The book aims to guide students preparing for competitive exams as well. The preface expresses gratitude to the original authors of referenced works and assures students that the book will be a helpful resource for both academic study and exam preparation.

• The book is tailored for B.Sc. Part I Mathematics, Paper III.
• Language is simple, engaging, and uses both Hindi and English terminology.
• Units are written by subject experts referencing standard texts.
• Useful for competitive exam preparation.
• Gratitude expressed to original authors of referenced materials.
• 📌 Co-ordinate Geometry: The branch of mathematics dealing with geometric figures using coordinates.
• 📌 Mathematical Programming: The study of optimization problems using mathematical techniques.

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)

Unit 1 deals with the reduction of the general second-degree Cartesian equation in X-Y to its standard forms. The unit outline includes objectives, introduction, definitions, transformation of axes by rotation, general equation of conic sections, theorems, special cases, center of conic sections, conditions for conic sections, summary, glossary, self-assessment questions, and exercises. The main focus is on understanding how to convert the general quadratic equation of two variables into standard forms representing conic sections such as straight lines, points, parabolas, and hyperbolas. The unit also covers finding the center of conic sections and determining the equation of the conic when the center is taken as the origin.

• Covers reduction of general quadratic equations in X-Y to standard forms.
• Includes definitions of conic sections and mathematical terminology.
• Explains transformation of axes by rotation.
• Discusses the general equation of conic sections and its reduction.
• Provides conditions for identifying conic sections.
• Includes methods to find the center of conic sections.
• 📌 Conic Section: A curve obtained as the intersection of 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 a conic section.