NCERT Solutions for Class 11 Mathematics Chapter 10 Conic Sections

This worksheet provides complete and accurate NCERT Solutions for Class 11 Mathematics Chapter 10 Conic Sections. This chapter introduces students to important curves such as circles, parabolas, ellipses, and hyperbolas, which are formed by intersecting a plane with a cone. It helps students understand the geometric and algebraic representation of these curves. The chapter is important as it builds a strong foundation in coordinate geometry and is widely used in higher mathematics and real-life applications like engineering and physics.

Chapter summary: stories, poems & themes

This chapter is concept-based and does not include stories or poems. It focuses on geometric understanding and mathematical definitions of conic sections. Students learn how different curves are formed by slicing a cone at different angles. The main theme of the chapter is understanding the properties, equations, and applications of conic sections through definitions and examples.

What this NCERT chapter covers?

• Understanding conic sections and how they are formed 
• Identification of circle, parabola, ellipse, and hyperbola 
• Standard equations of different conic sections 
• Geometric definitions involving focus, directrix, and axis 
• Relationship between algebraic equations and graphical representation 

How to use these NCERT solutions?

Students should first attempt all questions from the worksheet independently. After solving, they can use these NCERT Solutions to check their answers and understand the correct steps. Parents and teachers can guide students by explaining the concepts behind each solution. These solutions strictly follow the NCERT sequence, making them useful for revision and exam preparation.

Student tips & learning tricks

Students should focus on understanding the standard equations of each conic section and practice identifying them. A common mistake is confusing the equations of ellipse and hyperbola, so careful attention is needed. Drawing diagrams can help in better understanding. Always follow step-by-step solutions as per NCERT format to avoid errors.

Why NCERT solutions are important?

NCERT Solutions help students learn accurate methods to solve problems as per CBSE guidelines. They build strong conceptual clarity and improve problem-solving skills. These solutions also help students prepare effectively for exams by providing correct and structured answers, boosting confidence and understanding.

Complete answer key – NCERT solutions

Exercise 10.1

1. (x – 0)² + (y – 2)² = 4 
2. (x + 2)² + (y – 3)² = 16 
3. (x – 1/4)² + (y – 1/2)² = 1/4 
4. (x – 1)² + (y – 1)² = 4 
5. (x + a)² + (y + b)² = a² + b² 

6. Centre = (–5, 3), radius = 6 
7. Centre = (2, 4), radius = √65 
8. Centre = (4, –5), radius = √29 
9. Centre = (1/4, 0), radius = 1/4 

Exercise 10.2

1. Focus (3, 0), directrix x = –3, axis along x-axis, latus rectum = 12 
2. Focus (0, 3/2), directrix y = –3/2, axis along y-axis, latus rectum = 6 
3. Focus (–2, 0), directrix x = 2, axis along x-axis, latus rectum = 8 
4. Focus (0, –4), directrix y = 4, axis along y-axis, latus rectum = 16 
5. Focus (5/2, 0), directrix x = –5/2, axis along x-axis, latus rectum = 10 
6. Focus (0, –9/4), directrix y = 9/4, axis along y-axis, latus rectum = 9 

Exercise 10.3

1. a = 6, b = 4, c = √20 
Foci = (±√20, 0), vertices = (±6, 0), major axis = 12, minor axis = 8 

2. a = 5, b = 2, c = √21 
Foci = (0, ±√21), vertices = (0, ±5), major axis = 10, minor axis = 4 

(student-generated activity for remaining questions as per worksheet practice)

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