NCERT Solutions Class 11 Maths Chapter 10 guides you through Conic Sections with detailed solutions to all 70 questions covering circles, parabolas, ellipses, and hyperbolas. You’ll learn how to derive standard equations, find foci and directrix, identify conic types from equations, and solve coordinate geometry problems using section formulas. Each solution includes diagrams, formula derivations, and exam-focused shortcuts to help you tackle both theoretical and numerical questions confidently.
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All exercises with step-by-step solutions | Updated 2025-26 | Free Download
Download PDF (Free)NCERT Solutions Class 11 Maths Chapter 10 Conic Sections – Complete Guide
NCERT Class 11 Chapter 10 on Conic Sections introduces you to one of the most beautiful and practical topics in coordinate geometry. You’ll discover how circles, parabolas, ellipses, and hyperbolas are formed when a plane intersects a double-napped cone at different angles. This chapter builds a strong foundation for understanding curves that have countless applications in physics, engineering, astronomy, and architecture.
📊 CBSE Class 11 Maths Chapter 10 – Exam Weightage & Marking Scheme
| CBSE Board Marks | 6 Marks |
| Unit Name | Coordinate Geometry |
| Difficulty Level | Hard |
| Importance | High |
| Exam Types | CBSE Board, State Boards |
| Typical Questions | 2-3 questions |
You will learn to derive the standard equations of each conic section and understand their key properties—like foci, directrix, eccentricity, vertices, and axes. The chapter covers circles with their general and standard forms, parabolas opening in different directions, ellipses with horizontal and vertical orientations, and hyperbolas with their distinctive asymptotes. You’ll also explore how to convert between different forms of equations and identify conic sections from their general equations.
For CBSE board exams, this chapter carries significant weightage of 6 marks and is considered challenging yet highly scoring if you master the concepts. Expect a mix of 2-mark questions on basic definitions and properties, 4-mark problems on deriving equations or finding specific parameters, and 6-mark questions requiring complete analysis of conic sections. The questions often test your ability to apply formulas, visualize geometric relationships, and solve coordinate geometry problems systematically.
Quick Facts – Class 11 Chapter 10
| 📖 Chapter Number | Chapter 10 |
| 📚 Chapter Name | Conic Sections |
| ✏️ Total Exercises | 5 Exercises |
| ❓ Total Questions | 70 Questions |
| 📅 Updated For | CBSE Session 2025-26 |
Mastering Conic Sections will not only help you excel in your Class 11 exams but also prepare you for advanced topics in Class 12 and competitive examinations like JEE. The logical approach and problem-solving skills you develop here will serve you throughout your mathematical journey, making this chapter an essential milestone in your learning path.
NCERT Solutions Class 11 Maths Chapter 10 – All Exercises PDF Download
Download exercise-wise NCERT Solutions PDFs for offline study
| Exercise No. | Topics Covered | Download PDF |
|---|---|---|
| EXERCISE 10.1 | Complete step-by-step solutions for 15 questions | 📥 Download PDF |
| EXERCISE 10.2 | Complete step-by-step solutions for 12 questions | 📥 Download PDF |
| EXERCISE 10.3 | Complete step-by-step solutions for 20 questions | 📥 Download PDF |
| EXERCISE 10.4 | Complete step-by-step solutions for 15 questions | 📥 Download PDF |
| Miscellaneous Exercise on Chapter 10 | Complete step-by-step solutions for 8 questions | 📥 Download PDF |
Conic Sections – Key Formulas & Concepts
Quick reference for CBSE exams
| Formula | Description | When to Use |
|---|---|---|
| Equation of Circle (Standard Form) \((x – h)^2 + (y – k)^2 = r^2\) | Represents a circle with center (h, k) and radius r Note: Remember to square the radius (r) in the equation. If the center is at the origin (0,0), the equation simplifies to x² + y² = r². | When the center and radius of a circle are known, or need to be determined from the equation. |
| Parabola Equation (Rightward Opening) \(y^2 = 4ax\) | Equation of a parabola opening to the right, with vertex at (0,0) and focus at (a,0) Note: a is the distance from the vertex to the focus. The directrix is x = -a. | When the parabola opens to the right and its vertex is at the origin. Useful for finding focus, directrix, and length of latus rectum. |
| Parabola Equation (Leftward Opening) \(y^2 = -4ax\) | Equation of a parabola opening to the left, with vertex at (0,0) and focus at (-a,0) Note: a is the distance from the vertex to the focus. The directrix is x = a. | When the parabola opens to the left and its vertex is at the origin. |
| Parabola Equation (Upward Opening) \(x^2 = 4ay\) | Equation of a parabola opening upwards, with vertex at (0,0) and focus at (0,a) Note: a is the distance from the vertex to the focus. The directrix is y = -a. | When the parabola opens upwards and its vertex is at the origin. |
| Parabola Equation (Downward Opening) \(x^2 = -4ay\) | Equation of a parabola opening downwards, with vertex at (0,0) and focus at (0,-a) Note: a is the distance from the vertex to the focus. The directrix is y = a. | When the parabola opens downwards and its vertex is at the origin. |
| Ellipse Equation (Horizontal Major Axis) \(\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1\) | Equation of an ellipse centered at (0,0) with major axis along the x-axis (a > b) Note: a is the semi-major axis, b is the semi-minor axis. c² = a² – b², where c is the distance from the center to each focus. | When the ellipse is centered at the origin and the major axis is horizontal. Useful for finding vertices, foci, and eccentricity. |
| Ellipse Equation (Vertical Major Axis) \(\frac{x^2}{b^2} + \frac{y^2}{a^2} = 1\) | Equation of an ellipse centered at (0,0) with major axis along the y-axis (a > b) Note: a is the semi-major axis, b is the semi-minor axis. c² = a² – b², where c is the distance from the center to each focus. | When the ellipse is centered at the origin and the major axis is vertical. |
| Hyperbola Equation (Horizontal Transverse Axis) \(\frac{x^2}{a^2} – \frac{y^2}{b^2} = 1\) | Equation of a hyperbola centered at (0,0) with transverse axis along the x-axis Note: a is the distance from the center to each vertex. c² = a² + b², where c is the distance from the center to each focus. | When the hyperbola is centered at the origin and opens left and right. Useful for finding vertices, foci, and asymptotes. |
| Hyperbola Equation (Vertical Transverse Axis) \(\frac{y^2}{a^2} – \frac{x^2}{b^2} = 1\) | Equation of a hyperbola centered at (0,0) with transverse axis along the y-axis Note: a is the distance from the center to each vertex. c² = a² + b², where c is the distance from the center to each focus. | When the hyperbola is centered at the origin and opens up and down. |
| Eccentricity of Ellipse \(e = \frac{c}{a}\) | Calculates the eccentricity of an ellipse, where c is the distance from the center to the focus and a is the semi-major axis. Note: Remember that c² = a² – b² for an ellipse. Eccentricity close to 0 means the ellipse is close to a circle. | To determine how ‘stretched’ an ellipse is. e is always between 0 and 1. |
| Eccentricity of Hyperbola \(e = \frac{c}{a}\) | Calculates the eccentricity of a hyperbola, where c is the distance from the center to the focus and a is the distance from the center to the vertex. Note: Remember that c² = a² + b² for a hyperbola. | To determine how ‘wide’ a hyperbola is. e is always greater than 1. |
| Latus Rectum Length (Parabola) \(Length = 4a\) | Length of the latus rectum of the parabola Note: a is the distance from the vertex to the focus. | Finding the length of the line segment perpendicular to the axis of the parabola, passing through focus and whose end points lie on the parabola |
| Latus Rectum Length (Ellipse/Hyperbola) \(Length = \frac{2b^2}{a}\) | Length of the latus rectum of the ellipse or hyperbola. Note: a is the semi-major/transverse axis and b is the semi-minor/conjugate axis. | Finding the length of the line segment perpendicular to the major/transverse axis passing through the foci and whose end points lie on the conic section |
Frequently Asked Questions – NCERT Class 11 Maths Chapter 10
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