Chapter 10

प्रस्तावना

The book 'Co-ordinate Geometry and Mathematical Programming Problems' has been designed according to the curriculum proposed by Vardhman Mahaveer Open University, Kota, for the B.Sc. Part I Mathematics, Paper III. The language style of the book has been kept simple, interesting, and easy to understand. Considering the nature of Mathematics, appropriate use of English terminology has been made, and it was considered necessary to include essential vocabulary in both Hindi and English. Various units of the book have been written by expert authors, who have used standard references to ensure factual accuracy. The book aims to provide proper guidance for competitive examinations as well.

• The book is tailored for B.Sc. Part I Mathematics, Paper III.
• Simple and clear language is used for better understanding.
• English mathematical terms are included alongside Hindi.
• The book is useful for both academic study and competitive exams.
• 📌 Co-ordinate Geometry: The branch of mathematics dealing with the study of geometry using a coordinate system.
• 📌 Mathematical Programming: The process of solving mathematical problems (often optimization) using mathematical models and 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)

This unit focuses on the reduction of the general second-degree equation in two variables (x and y) to its standard forms. The general equation is given as: ax^2 + 2hxy + by^2 + 2gx + 2fy + c = 0 The main objective is to determine the type of conic section represented by a given general quadratic equation and to reduce it to its standard form. The unit also covers the determination of the center of the conic section and the equation of the conic when the center is taken as the origin.

• Reduction of general second-degree equation to standard forms.
• Identification of conic sections (straight lines, point, parabola, hyperbola, etc.).
• Finding the center of the conic section.
• Equation of the conic relative to axes passing through the center.
• 📌 General Quadratic Equation: An equation of the form ax^2 + 2hxy + by^2 + 2gx + 2fy + c = 0.
• 📌 Conic Section: The locus of a point which moves so that its distance from a fixed point (focus) bears a constant ratio to its distance from a fixed straight line (directrix).