The NCERT Solutions for Class 11 Maths Chapter 10 Conic Sections Exercise 10.2 cover every question on the parabola, 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 10.2 is the parabola section of Conic Sections. The exercise has 12 questions built around these skills:
- Reading the focus, axis, directrix and latus rectum from a standard parabola.
- Matching an equation to the correct one of the four standard forms.
- Building a parabola's equation from a given focus, directrix or vertex condition.
Topics Covered in Exercise 10.2
This exercise develops the parabola, the set of points equidistant from a fixed point (the focus) and a fixed line (the directrix). Exercise 10.2 works entirely with parabolas whose vertex is at the origin and whose axis is a coordinate axis, so the four standard forms are the whole toolkit for the NCERT Solutions for Class 11 Maths Chapter 10 Conic Sections Exercise 10.2.
- Four standard forms: y2 = 4ax, y2 = −4ax, x2 = 4ay and x2 = −4ay.
- Focus and directrix: for y2 = 4ax the focus is (a, 0) and the directrix is x = −a.
- Latus rectum: the chord through the focus perpendicular to the axis, of length 4a.
- Axis of symmetry: the coordinate axis the parabola opens along.
Important: the sign of the term and which variable is squared decide the direction in which the parabola opens, so identify the standard form before reading off any value.
Question-wise Breakdown of Exercise 10.2
The NCERT Solutions for Class 11 Maths Chapter 10 Conic Sections Exercise 10.2 solve all 12 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 to Q6 | Find focus, axis, directrix and length of latus rectum of a given parabola | Reading a standard form |
| Q7, Q8 | Find the equation from a given focus and directrix | Definition of a parabola |
| Q9, Q10 | Find the equation from vertex (0, 0) and a given focus | Choosing the right form |
| Q11, Q12 | Find the equation of a parabola passing through a given point with a stated axis | Fixing the value of a |
The first six questions are quick reading exercises, while the last six ask students to build an equation from geometric data.
Key Formulas and Definitions for Exercise 10.2
Exercise 10.2 rests on the four standard forms of a parabola and the results that follow from each. Students should keep this table ready while solving.
| Standard form | Focus / Directrix / Latus rectum |
|---|---|
| y2 = 4ax (opens right) | Focus (a, 0); directrix x = −a; latus rectum 4a |
| y2 = −4ax (opens left) | Focus (−a, 0); directrix x = a; latus rectum 4a |
| x2 = 4ay (opens up) | Focus (0, a); directrix y = −a; latus rectum 4a |
| x2 = −4ay (opens down) | Focus (0, −a); directrix y = a; latus rectum 4a |
| Vertex | (0, 0) for every standard form in this exercise |
Tip: to find a, compare the given equation with its standard form, for example y2 = 12x gives 4a = 12, so a = 3.
Common Mistakes in Exercise 10.2
Students lose easy marks in Exercise 10.2 on direction and sign errors. 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 10.2.
- Confusing the two axes: y2 = 4ax opens along the x-axis, while x2 = 4ay opens along the y-axis.
- Getting the sign of the directrix wrong. For y2 = 4ax the directrix is x = −a, not x = a.
- Reporting the latus rectum as a instead of 4a.
- Choosing the wrong standard form when a parabola opens left or down, which needs the negative sign.
Practice Questions for Exercise 10.2
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 10.2.
Practice Card: Solved Practice Questions for Class 11 Maths Conic Sections Exercise 10.2 — 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 10.2 is done.
| Exercise | NCERT Solutions link |
|---|---|
| Exercise 10.1 | Class 11 Maths Conic Sections Exercise 10.1 Solutions |
| Exercise 10.3 | Class 11 Maths Conic Sections Exercise 10.3 Solutions |
| Exercise 10.4 | Class 11 Maths Conic Sections Exercise 10.4 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, 66% of students said choosing the correct standard form for parabolas that open left or down in Exercise 10.2 was the trickiest step, while reading off the latus rectum was rated the easiest.
FAQs on NCERT Solutions for Class 11 Maths Chapter 10 Conic Sections Exercise 10.2
Conic Sections NCERT Solutions - Frequently Asked Questions
Ques. How many questions are there in Class 11 Maths Chapter 10 Conic Sections Exercise 10.2?
Ans. Exercise 10.2 has 12 questions on the parabola. The first six ask for the focus, axis, directrix and latus rectum of a given parabola, and the last six ask students to build the equation of a parabola from a focus, directrix or vertex condition.
Ques. What are the four standard forms of a parabola in Exercise 10.2?
Ans. The four standard forms are y2 = 4ax (opens right), y2 = −4ax (opens left), x2 = 4ay (opens up) and x2 = −4ay (opens down). Each has its vertex at the origin.
Ques. What is the length of the latus rectum of a parabola?
Ans. The latus rectum is the chord through the focus that is perpendicular to the axis, and its length is 4a. For y2 = 12x, comparing gives 4a = 12, so the latus rectum is 12 units long.
Ques. How do I find the equation of a parabola from its focus and directrix?
Ans. Use the definition: a point on the parabola is equidistant from the focus and the directrix. Equating the two distances and simplifying gives the standard form. Questions 7 and 8 use this method directly.
Ques. Are the NCERT Solutions for Class 11 Maths Chapter 10 Conic Sections Exercise 10.2 free to download?
Ans. Yes. The NCERT Solutions for Class 11 Maths Chapter 10 Conic Sections Exercise 10.2 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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