The NCERT Solutions for Class 11 Maths Chapter 10 Conic Sections Exercise 10.1 cover every question on the circle, 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 10.1 is the circle section of Conic Sections. The exercise has 15 questions built around these skills:
- Writing the standard equation of a circle from its centre and radius.
- Reading the centre and radius back from a given equation.
- Finding a circle from conditions such as points it passes through or where its centre lies.
Topics Covered in Exercise 10.1
This exercise introduces the circle as a conic section. A circle is the set of all points in a plane that are at a fixed distance, the radius, from a fixed point, the centre. Exercise 10.1 moves between the standard form, the general form and simple geometric conditions on the NCERT Solutions for Class 11 Maths Chapter 10 Conic Sections Exercise 10.1.
- Standard equation: a circle with centre (h, k) and radius r is (x − h)2 + (y − k)2 = r2.
- Circle at the origin: when the centre is (0, 0) this becomes x2 + y2 = r2.
- General equation: x2 + y2 + 2gx + 2fy + c = 0, which is turned into standard form by completing the square.
- Geometric conditions: a circle fixed by points it passes through together with a line on which its centre lies.
Important: to read the centre and radius from a general equation, first make the coefficients of x2 and y2 both equal to 1, then complete the square.
Question-wise Breakdown of Exercise 10.1
The NCERT Solutions for Class 11 Maths Chapter 10 Conic Sections Exercise 10.1 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 to Q5 | Find the equation of a circle from a given centre and radius | Standard equation |
| Q6 to Q9 | Find the centre and radius of a given circle | Completing the square |
| Q10, Q11 | Circle through two points with centre on a given line | Solving conditions together |
| Q12 | Radius 5, centre on the x-axis, passing through (2, 3) | Centre on an axis |
| Q13 | Circle through the origin making given intercepts on the axes | Intercept form |
| Q14, Q15 | Circle through a point; testing if a point lies inside | Distance and radius |
The early questions are direct substitution, while the later ones ask students to set up and solve two conditions at once.
Key Formulas and Definitions for Exercise 10.1
Exercise 10.1 rests on the standard and general equations of a circle. Students should learn these results before attempting the questions.
| Term / Formula | Meaning |
|---|---|
| (x − h)2 + (y − k)2 = r2 | Circle with centre (h, k) and radius r |
| x2 + y2 = r2 | Circle with centre at the origin |
| x2 + y2 + 2gx + 2fy + c = 0 | General equation of a circle |
| Centre = (−g, −f) | Centre from the general equation |
| Radius = √(g2 + f2 − c) | Radius from the general equation |
| Distance = √((x2 − x1)2 + (y2 − y1)2) | Distance between two points |
Tip: a point lies inside, on or outside a circle when its distance from the centre is less than, equal to or greater than the radius.
Common Mistakes in Exercise 10.1
Students lose easy marks in Exercise 10.1 on small slips of sign and setup. 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 10.1.
- Forgetting the sign flip: the centre from the general equation is (−g, −f), not (g, f).
- Skipping the step of making the coefficients of x2 and y2 equal to 1 before completing the square, as in Question 9.
- Writing the radius as r2 instead of r when forming the equation, or the reverse when reading it.
- In the two-condition problems, using only the points and ignoring the line that fixes the centre.
Practice Questions for Exercise 10.1
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 10.1.
Practice Card: Solved Practice Questions for Class 11 Maths Conic Sections Exercise 10.1 — 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 10.1 is done.
| Exercise | NCERT Solutions link |
|---|---|
| Exercise 10.2 | Class 11 Maths Conic Sections Exercise 10.2 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, 64% of students said completing the square to find the centre and radius in Exercise 10.1 was the step they slipped on most, while writing the standard equation was rated the easiest.
FAQs on NCERT Solutions for Class 11 Maths Chapter 10 Conic Sections Exercise 10.1
Conic Sections NCERT Solutions - Frequently Asked Questions
Ques. How many questions are there in Class 11 Maths Chapter 10 Conic Sections Exercise 10.1?
Ans. Exercise 10.1 has 15 questions on the circle. The first group asks students to write the equation of a circle from its centre and radius, the middle group asks for the centre and radius of given circles, and the last group fixes a circle from points and lines.
Ques. What is the standard equation of a circle in Exercise 10.1?
Ans. A circle with centre (h, k) and radius r has the equation (x − h)2 + (y − k)2 = r2. When the centre is at the origin this reduces to x2 + y2 = r2.
Ques. How do I find the centre and radius from the general equation?
Ans. For x2 + y2 + 2gx + 2fy + c = 0 the centre is (−g, −f) and the radius is √(g2 + f2 − c). If the coefficients of x2 and y2 are not 1, divide through first.
Ques. How do I check whether a point lies inside a circle?
Ans. Find the distance of the point from the centre. If it is less than the radius the point is inside, if equal it lies on the circle, and if greater it is outside. Question 15 uses this test for the point (−2.5, 3.5) on x2 + y2 = 25.
Ques. Are the NCERT Solutions for Class 11 Maths Chapter 10 Conic Sections Exercise 10.1 free to download?
Ans. Yes. The NCERT Solutions for Class 11 Maths Chapter 10 Conic Sections Exercise 10.1 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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