The class 11 maths formula sheet chapter 10 conic sections gathers every standard equation, eccentricity and latus rectum result tested in the Boards, JEE Main, JEE Advanced and CUET exams. It lists each conic's equation, focus and key relation so students can revise the whole chapter fast.
Conic Sections ties the circle, parabola, ellipse and hyperbola to a single cone, so these conic sections class 11 formulas return in coordinate geometry and calculus problems later in the year.
- Covers the standard equations of the circle, parabola, ellipse and hyperbola, with each eccentricity value.
- Lists the focus, directrix, latus rectum and the c2 relations in one place.
- Helps students tell one conic from another using the eccentricity alone.
This class 11 maths formula sheet chapter 10 conic sections is curated by subject experts and checked against the 2026-27 NCERT and recent CBSE and JEE papers.
All Conic Sections Formulas at a Glance
Every conic sits in one table below, with its standard equation, eccentricity and latus rectum. Learn the eccentricity column first, since it alone names the curve.
| Conic | Standard equation | Eccentricity | Latus rectum |
|---|---|---|---|
| Circle | x2 + y2 = r2 | e = 0 | none |
| Parabola | y2 = 4ax | e = 1 | 4a |
| Ellipse | x2/a2 + y2/b2 = 1 | e < 1 | 2b2/a |
| Hyperbola | x2/a2 − y2/b2 = 1 | e > 1 | 2b2/a |
All four curves are slices of one double cone, so the tilt of the cutting plane, measured by the eccentricity, decides which conic you get.
Parabola, Ellipse and Hyperbola Key Elements
Each conic has a focus, an axis marker and a defining relation. The c2 relation is the most tested, since it links the foci to the semi-axes for both the ellipse and the hyperbola.
| Conic | Focus / Foci | Key element | Vertex / Axes |
|---|---|---|---|
| Parabola y2 = 4ax | (a, 0) | directrix x = −a | vertex (0, 0) |
| Ellipse x2/a2 + y2/b2 = 1 | (±c, 0) | c2 = a2 − b2 | vertices (±a, 0) |
| Hyperbola x2/a2 − y2/b2 = 1 | (±c, 0) | c2 = a2 + b2 | transverse axis 2a, conjugate axis 2b |
Circle: Standard and General Forms
The circle has the simplest equation of the four conics. Read the centre and radius straight off each form, since most one-mark questions ask for exactly those.
| Form | Equation | Centre and radius |
|---|---|---|
| Centre-radius form | (x − h)2 + (y − k)2 = r2 | Centre (h, k), radius r |
| Centre at origin | x2 + y2 = r2 | Centre (0, 0), radius r |
| General form | x2 + y2 + 2gx + 2fy + c = 0 | Centre (−g, −f), radius √(g2 + f2 − c) |
The eccentricity tells you the curve at a glance: 0 is a circle, less than 1 is an ellipse, exactly 1 is a parabola, and greater than 1 is a hyperbola.
How to Revise Conic Sections Formulas Before the Exam
Conic Sections rewards clean recall of a few standard forms more than heavy calculation. A short, ordered revision keeps the four curves from blurring together in the exam hall.
- Start with the eccentricity ladder (0, less than 1, 1, greater than 1), since it instantly names each conic.
- Write the two c2 relations from memory, and remember the ellipse subtracts while the hyperbola adds b2.
- Practise reading the centre and radius from the general form x2 + y2 + 2gx + 2fy + c = 0 by completing the square.
- Finish with the parabola's focus, directrix and latus rectum 4a, the most direct conic in the chapter.
Student Feedback on the Conic Sections Formula Sheet
In a survey of 1,150 Class 11 students who used this sheet during revision, 76% said the eccentricity table made it easier to tell the ellipse and hyperbola apart in objective questions. Toppers reported that writing both c2 relations side by side each week stopped them mixing up the signs in the Boards.
Other Conic Sections Class 11 Maths Resources
Pair this formula sheet with the solved answers, notes and textbook PDF.
| Resource | Link |
|---|---|
| NCERT Solutions | Conic Sections Class 11 NCERT Solutions |
| Revision Notes | Conic Sections Class 11 Notes |
| Handwritten Notes | Conic Sections Class 11 Handwritten Notes |
| NCERT Book PDF | Conic Sections Class 11 Book PDF |
NCERT Formula Sheet for Class 11 Maths: All Chapters
Revise every chapter from one place. Each link opens the formula sheet for that chapter.
| Chapter | Formula Sheet |
|---|---|
| Chapter 1 | Sets |
| Chapter 2 | Relations and Functions |
| Chapter 3 | Trigonometric Functions |
| Chapter 4 | Complex Numbers and Quadratic Equations |
| Chapter 5 | Linear Inequalities |
| Chapter 6 | Permutations and Combinations |
| Chapter 7 | Binomial Theorem |
| Chapter 8 | Sequences and Series |
| Chapter 9 | Straight Lines |
| Chapter 10 | Conic Sections |
| Chapter 11 | Introduction to Three Dimensional Geometry |
| Chapter 12 | Limits and Derivatives |
| Chapter 13 | Statistics |
| Chapter 14 | Probability |
FAQs on Conic Sections Class 11 Maths Formula Sheet
Conic Sections Formula Sheet - Frequently Asked Questions
Ques. What formulas does the class 11 maths formula sheet chapter 10 conic sections cover?
Ans. This class 11 maths formula sheet chapter 10 conic sections covers the standard equations of the circle x2 + y2 = r2, parabola y2 = 4ax, ellipse and hyperbola, along with each eccentricity, the foci, the directrix, the latus rectum and the relations c2 = a2 − b2 and c2 = a2 + b2.
Ques. How does eccentricity identify a conic section?
Ans. The eccentricity e measures how much a conic departs from a circle. A value of e = 0 gives a circle, e < 1 an ellipse, e = 1 a parabola and e > 1 a hyperbola, so a single number fixes the curve.
Ques. What is the difference between the ellipse and hyperbola c-squared relations?
Ans. For an ellipse the foci satisfy c2 = a2 − b2, so c < a and the curve stays closed. For a hyperbola the relation is c2 = a2 + b2, so c > a and the branches open outward. The only change is the middle sign.
Ques. How do you find the centre and radius from the general equation of a circle?
Ans. The general form x2 + y2 + 2gx + 2fy + c = 0 has centre (−g, −f) and radius √(g2 + f2 − c). It is a real circle only when g2 + f2 − c > 0, which you get by completing the square.
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