MATC-203 YCMOU Assignment Answers 2026-27

Earn 30% of your MATC-203 CA marks effortlessly with this YCMOU-approved solved assignment guide, meticulously crafted for B.Sc. (Honours) Mathematics students following the 2025 Pattern syllabus. Designed to eliminate guesswork in Home Assignments (गृहपाठ), this resource ensures you submit flawless solutions that align with YCMOU’s Continuous Assessment criteria, saving time and boosting your grade before the Term-End Exam (TEE).

Course Overview & Academic Objective

MATC-203 – Coordinate Geometry – is a core component of the B.Sc. (Honours) Mathematics curriculum at YCMOU, focusing on the theoretical and applied aspects of coordinate systems, transformations, and geometric properties. Students learn to solve complex problems using Cartesian, polar, and parametric coordinates while developing rigorous proof techniques. This assignment guide directly supports the academic objective of mastering analytical geometry, a prerequisite for advanced topics in calculus and algebraic geometry.

Key Syllabus Modules & Chapters Covered

The guide comprehensively addresses all mandatory chapters from the MATC-203 syllabus, including:

• Chapter 1: Coordinate Geometry in Two Dimensions
  • Derivation of distance, section formula, and locus of a point with exact algebraic proofs (e.g., proof of the condition for collinearity: ax + by + c = 0)
  • Application of parametric equations to find chord lengths and angle bisectors in triangles
• Chapter 2: Coordinate Geometry in Three Dimensions
  • Vector algebra solutions for plane and line equations, including the derivation of the angle between two planes using direction cosines
  • Step-by-step solutions for shortest distance problems between skew lines (e.g., d = |(a_1 – a_2) · (b_1 × b_2)| / |b_1 × b_2|)
• Chapter 3: Transformation Geometry
  • Transformation matrices for rotation, translation, and reflection with geometric interpretations (e.g., rotation of axes to eliminate xy-term in conic sections)
  • Solutions for homogeneous coordinate systems and their applications in projective geometry
• Chapter 4: Applications to Curves and Surfaces
  • Parametric representations of ellipse, hyperbola, and parabola with focus on eccentricity calculations
  • Surface area and volume integrals for quadric surfaces (e.g., ellipsoid, hyperboloid) using double integrals

Continuous Assessment & Exam Utility

This guide is exclusively tailored to YCMOU’s CA framework, where Home Assignments (गृहपाठ) contribute 30% of your total CA score. Each solution adheres to:

• Problem-Specific Formatting: Answers follow YCMOU’s structured solution format, including:
• Clear step numbering with logical progression
• Use of YCMOU-approved symbols (e.g., ∴ for