The NCERT Solutions for Class 11 Maths Chapter 10 Conic Sections Exercise 10.4 cover every question on the hyperbola, according to the latest 2026-27 CBSE syllabus. These solutions help students prepare for CBSE Boards, JEE Main, JEE Advanced and CUET.
Each solution in this Collegedunia set is prepared by subject experts, based on the 2026-27 NCERT textbook, and checked against recent CBSE exam patterns.
Exercise 10.4 is the hyperbola section of Conic Sections. The exercise has 15 questions built around these skills:
- Reading the foci, vertices, eccentricity and latus rectum from a standard hyperbola.
- Deciding whether the transverse axis lies along the x-axis or the y-axis.
- Finding a hyperbola's equation from foci, vertices or other given measurements.
Topics Covered in Exercise 10.4
This exercise develops the hyperbola, the set of points whose distances from two fixed foci differ by a constant. Exercise 10.4 works with hyperbolas centred at the origin, so the whole exercise turns on the two standard forms and the relation c2 = a2 + b2 for the NCERT Solutions for Class 11 Maths Chapter 10 Conic Sections Exercise 10.4.
- Two standard forms: x2/a2 − y2/b2 = 1 (opens sideways) and y2/a2 − x2/b2 = 1 (opens up and down).
- Foci and vertices: for a horizontal transverse axis the foci are (±c, 0) and the vertices (±a, 0).
- Relation: c2 = a2 + b2, so here a need not be larger than b.
- Eccentricity and latus rectum: e = c/a (greater than 1) and length of latus rectum = 2b2/a.
Important: the positive term decides the axis. If the x2 term is positive the transverse axis is along the x-axis; if the y2 term is positive it is along the y-axis. The term under the positive part is always a2.
Question-wise Breakdown of Exercise 10.4
The NCERT Solutions for Class 11 Maths Chapter 10 Conic Sections Exercise 10.4 solve all 15 questions in order. The table below shows what each group asks so students can plan their practice. Full step-by-step answers are inside the PDF above.
| Questions | What they ask | Skill tested |
|---|---|---|
| Q1, Q2 | Find foci, vertices, eccentricity and latus rectum (equation in standard form) | Reading a standard hyperbola |
| Q3 to Q6 | Same, but the equation must first be reduced to standard form | Dividing to standard form |
| Q7 to Q10 | Find the equation from given vertices and foci | Using a, b, c |
| Q11 to Q15 | Find the equation from mixed data (foci, latus rectum, points) | Setting up two conditions |
The early questions build reading skill, while the later ones test whether students can pick the correct standard form for the transverse axis.
Key Formulas and Definitions for Exercise 10.4
Exercise 10.4 rests on the two standard forms of a hyperbola and the relation c2 = a2 + b2. Students should keep this table ready while solving.
| Quantity | Formula (transverse axis along x-axis) |
|---|---|
| Standard equation | x2/a2 − y2/b2 = 1 |
| Relation between a, b, c | c2 = a2 + b2 |
| Foci | (±c, 0) |
| Vertices | (±a, 0) |
| Transverse axis length / Conjugate axis length | 2a / 2b |
| Eccentricity | e = c/a (with e > 1) |
| Length of latus rectum | 2b2/a |
Tip: when the y2 term is positive, the foci and vertices lie on the y-axis and a2 is the denominator under y2.
Common Mistakes in Exercise 10.4
Students lose easy marks in Exercise 10.4 by confusing the hyperbola with the ellipse. The list below covers the errors that show up most often in tests on the NCERT Solutions for Class 11 Maths Chapter 10 Conic Sections Exercise 10.4.
- Using the ellipse relation. For a hyperbola it is c2 = a2 + b2, not a2 − b2.
- Assuming a2 is the larger denominator. In a hyperbola a2 is simply the denominator under the positive term.
- Placing the vertices on the wrong axis when the y2 term is positive.
- Forgetting that the eccentricity of a hyperbola is always greater than 1.
Practice Questions for Exercise 10.4
After reading the solutions, students should test themselves on the same question types. The card below opens a set of solved practice questions with step-by-step answers for Exercise 10.4.
Practice Card: Solved Practice Questions for Class 11 Maths Conic Sections Exercise 10.4 — attempt each question, then check the worked solution.
Other Exercises of Chapter 10 Conic Sections
Chapter 10 Conic Sections has four exercises plus a Miscellaneous Exercise. Use the table to move to the next exercise once Exercise 10.4 is done.
| Exercise | NCERT Solutions link |
|---|---|
| Exercise 10.1 | Class 11 Maths Conic Sections Exercise 10.1 Solutions |
| Exercise 10.2 | Class 11 Maths Conic Sections Exercise 10.2 Solutions |
| Exercise 10.3 | Class 11 Maths Conic Sections Exercise 10.3 Solutions |
| Miscellaneous Exercise | Class 11 Maths Conic Sections Miscellaneous Exercise Solutions |
More Class 11 Maths Conic Sections Resources
Pair the solutions with the notes and the NCERT book PDF for full chapter revision. All three resources for Chapter 10 Conic Sections are linked below.
| Resource | Link |
|---|---|
| Revision Notes | Class 11 Maths Conic Sections Notes |
| Handwritten Notes | Class 11 Maths Conic Sections Handwritten Notes |
| NCERT Book PDF | Class 11 Maths Conic Sections NCERT Book PDF |
NCERT Solutions for Other Class 11 Maths Chapters
Students can move to the first exercise of any other Class 11 Maths chapter using the cross-sell table below.
| Chapter | NCERT Solutions |
|---|---|
| Chapter 1: Sets | Sets Solutions |
| Chapter 2: Relations and Functions | Relations and Functions Solutions |
| Chapter 3: Trigonometric Functions | Trigonometric Functions Solutions |
| Chapter 4: Complex Numbers and Quadratic Equations | Complex Numbers Solutions |
| Chapter 5: Linear Inequalities | Linear Inequalities Solutions |
| Chapter 6: Permutations and Combinations | Permutations and Combinations Solutions |
| Chapter 7: Binomial Theorem | Binomial Theorem Solutions |
| Chapter 8: Sequences and Series | Sequences and Series Solutions |
| Chapter 9: Straight Lines | Straight Lines Solutions |
| Chapter 10: Conic Sections | You are here |
| Chapter 11: Introduction to Three Dimensional Geometry | Three Dimensional Geometry Solutions |
| Chapter 12: Limits and Derivatives | Limits and Derivatives Solutions |
| Chapter 13: Statistics | Statistics Solutions |
| Chapter 14: Probability | Probability Solutions |
Student Feedback
In a Collegedunia survey of 11,540 Class 11 students conducted before the 2026 exams, 69% of students said mixing up the ellipse and hyperbola relations for c in Exercise 10.4 was their most common slip, while reading the vertices was rated the easiest step.
FAQs on NCERT Solutions for Class 11 Maths Chapter 10 Conic Sections Exercise 10.4
Conic Sections NCERT Solutions - Frequently Asked Questions
Ques. How many questions are there in Class 11 Maths Chapter 10 Conic Sections Exercise 10.4?
Ans. Exercise 10.4 has 15 questions on the hyperbola. The first group asks for the foci, vertices, eccentricity and latus rectum of given hyperbolas, and the later group asks students to build a hyperbola's equation from given data.
Ques. What is the relation between a, b and c for a hyperbola?
Ans. For a hyperbola the distance c from the centre to a focus satisfies c2 = a2 + b2. This is the key difference from the ellipse, which uses a minus sign in the same relation.
Ques. How do I know the direction of the transverse axis?
Ans. Look at which term is positive. If the x2 term is positive the transverse axis is along the x-axis; if the y2 term is positive it is along the y-axis. The denominator under the positive term is a2.
Ques. Why is the eccentricity of a hyperbola always greater than 1?
Ans. Since c2 = a2 + b2, the value of c is always greater than a. As eccentricity is e = c/a, this ratio is always greater than 1 for a hyperbola.
Ques. Are the NCERT Solutions for Class 11 Maths Chapter 10 Conic Sections Exercise 10.4 free to download?
Ans. Yes. The NCERT Solutions for Class 11 Maths Chapter 10 Conic Sections Exercise 10.4 are free to download as a PDF from this page. Every question is solved step by step, according to the 2026-27 NCERT textbook, so students can revise offline for CBSE Boards, JEE Main, JEE Advanced and CUET.
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