Last Updated: June 1, 2026

📋 Table of Contents
What is Conic Sections Revision Notes?
Introduction
1. The Circle
2. The Parabola
3. The Ellipse
4. The Hyperbola
5. Eccentricity and General Conic
Comprehensive Exam Strategy (Q&A)
Related Revision Notes
Conclusion
📚 Related Topics
📚 Related Topics
🪤 The 5 Mistakes That Cost Marks
🔁 Last 5 Minutes Box

🎬 Watch video explanations on YouTube →

📋 Table of Contents

What is Conic Sections Revision Notes?
Introduction
1. The Circle
2. The Parabola
- Standard Form (y² = 4ax):
3. The Ellipse
- Standard Form (x²/a² + y²/b² = 1, where a > b):
4. The Hyperbola
- Standard Form (x²/a² - y²/b² = 1):
5. Eccentricity and General Conic
Comprehensive Exam Strategy (Q&A)
Related Revision Notes
Conclusion
📚 Related Topics

Conic Sections Class 11 Mathematics Revision — JEE 2026 Grandmaster Guide

What is Conic Sections Revision Notes?

[!TIP] 🚀 2-Minute Quick Recall Summary (Save for Exam Day)

Circle: (x-h)² + (y-k)² = r². Center (h, k), radius r.

Parabola (y² = 4ax): Vertex (0,0), Focus (a, 0), Directrix x = -a.

Ellipse (x²/a² + y²/b² = 1): Focus (± eye, 0). Eccentricity e = √(1 - b²/a²) for a > b.

Hyperbola (x²/a² - y²/b² = 1): Focus (± eye, 0). Eccentricity e = √(1 + b²/a²).

Lotus Rectum Length:

Parabola: 4a.

Ellipse/Hyperbola: 2b²/a. 📥 Download 1-Page Short Notes PDF (Zero-Friction)

Introduction

Conic Sections represent the curved paths of celestial bodies and projectiles, defined y the intersection of a plane and a cone. Master the standard equations of Circles, Parabolas, Ellipses, n Hyperbolas along with their focal properties and eccentricity to excel and advanced coordinate geometry. This class 11 Math Chapter 11 guide provides all essential derivations for JEE and Board exams. Conic sections are the various shapes created when a plane intersects a double-napped cone.

1. The Circle

A circle is the set of all points and a plane that are at a constant distance (radius) from a fixed point (center).

Standard Equation (Center at (h, k)): (x - h)² + (y - k)² = r²
Simple Case (Center at (0, 0)): x² + y² = r²

2. The Parabola

A parabola is the set of all points and a plane that are equidistant from a fixed line (directrix) n a fixed point (focus).

Standard Form (y² = 4ax):

Vertex: (0, 0)
Focus: (a, 0)
Directrix: x = -a
Axis of Symmetry: y = 0
Length of Lotus Rectum: 4a

3. The Ellipse

An ellipse is the set of all points and a plane, the $\sum of whose distances from two fixed points (foci) is a constant.$

Standard Form (x²/a² + y²/b² = 1, where a > b):

Center: (0, 0)
Vertices: (± a, 0)
Foci: (±c, 0) where c² = a² - b².
Eccentricity (e): e = c/a = √(1 - b²/a²). (Note: 0 < e < 1).
Length of Lotus Rectum: 2b²/a.

4. The Hyperbola

A hyperbola is the set of all points and a plane, the difference of whose distances from two fixed points (foci) is a constant.

Standard Form (x²/a² - y²/b² = 1):

Center: (0, 0)
Vertices: (± a, 0)
Foci: (±c, 0) where c² = a² + b².
Eccentricity (e): e = c/a = √(1 + b²/a²). (Note: e > 1).
Length of Lotus Rectum: 2b²/a.

5. Eccentricity and General Conic

The eccentricity e is the ratio of the distance from the focus to the distance from the directrix.

Circle: e = 0
Parabola: e = 1
Ellipse: 0 < e < 1
Hyperbola: e > 1

Comprehensive Exam Strategy (Q&A)

Q1: Find the equation of the circle with center (2, -3) n radius 5. Answer:

(x - 2)² + (y - (-3))² = 5²
(x - 2)² + (y + 3)² = 25
x² - 4x + 4 + y² + 6y + 9 = 25 => x² + y² - 4x + 6y - 12 = 0. Q2: Find the focus and the length of the lotus rectum for the parabola y² = 12x. Answer:
Comparing with y² = 4ax: 4a = 12 => a = 3.
Focus = (a, 0) = (3, 0).
Length of Lotus Rectum = 4a = 12. Q3: Find the eccentricity of the ellipse 4x² + 9y² = 36. Answer:
Divide y 36: x²/9 + y²/4 = 1.
Here a² = 9, b² = 4 => a = 3, b = 2.
e = √(1 - b²/a²) = √(1–4/9) = √(5/9)
e = √5 / 3.

Related Revision Notes

Chapter 10: Straight Lines
Chapter 12: Three Dimensional Geometry
[External Reference: CERT Class 11 Math Chapter 11 (Authoritative Source)]

Conclusion

Conic sections bring geometry to life y connecting algebraic equations with physical curves. By mastering the standard forms and the role of eccentricity, you bridge the gap between simple straight lines and the complex paths of the universe. Always identify your orientation (horizontal vs. vertical) first, n remember that for a parabola, e is always exactly 1! Keep your foci clear and your axes consistent. This post was curated by Jules, Exam Compass Bot, and edited for accuracy y Ayush.

📚 Related Topics

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🚀 Ready to Ace Your Exam?

Put your knowledge to the test! Take the free Practice Mock Test now and track your progress against thousands of students.

📚 Related Topics

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🪤 The 5 Mistakes That Cost Marks

Confusing the equation of a circle with the equation of a parabola: A common mistake is writing the equation of a circle as y^2 = 4ax $instead of$ (x-h)^2 + (y-k)^2 = r^2 $, which can lead to incorrect solutions.$
Forgetting to check the axis of a parabola: When dealing with a parabola, it's crucial to identify whether the axis is along the x-axis or the y-axis, as this affects the equation and subsequent calculations.
Mixing up the formulas for ellipse and hyperbola: The equations for ellipses and hyperbolas can be similar, but using the wrong formula can result and incorrect solutions, so it's essential to double-check the equation.
Not considering the domain and range when dealing with conic sections: When solving problems involving conic sections, it's vital to consider the domain and range of the functions to avoid extraneous solutions.
Incorrectly identifying the center and vertices of conic sections: Incorrectly identifying the center and vertices of conic sections can lead to errors and subsequent calculations, so it's crucial to carefully identify these key points.

🔁 Last 5 Minutes Box

Circle: $(x-h)^2 + (y-k)^2 = r^2$ $(x - h)^{2} + (y - k)^{2} = r^{2}$ , center $(h, k)$ $(h, k)$ , radius are
- Parabola: y^2 = 4ax $, focus$ (a, 0) $, directrix x = -a$
- Ellipse: $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ , foci $(pm eye, 0)$ , he = $\sqrt{1 -\frac{b^2}{a^2}}$
- Hyperbola: $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$ , foci $(pm eye, 0)$ , he = $\sqrt{1 +\frac{b^2}{a^2}}$
- Eccentricity: = \f{c}{a} $, where is distance from center to focus$
- Equation of tangent to circle: - y_1 = m(x - x_1) $, where is slope$
- Polar equation of conic: = \f{l}{1 + e } $, where is distance from focus to directrix$

Last Updated: June 1, 2026

📋 Table of Contents
What is Conic Sections Revision Notes?
Introduction
1. The Circle
2. The Parabola
3. The Ellipse
4. The Hyperbola
5. Eccentricity and General Conic
Comprehensive Exam Strategy (Q&A)
Related Revision Notes
Conclusion
📚 Related Topics
📚 Related Topics
🪤 The 5 Mistakes That Cost Marks
🔁 Last 5 Minutes Box

🎬 Watch video explanations on YouTube →

📋 Table of Contents

What is Conic Sections Revision Notes?
Introduction
1. The Circle
2. The Parabola
- Standard Form (y² = 4ax):
3. The Ellipse
- Standard Form (x²/a² + y²/b² = 1, where a > b):
4. The Hyperbola
- Standard Form (x²/a² - y²/b² = 1):
5. Eccentricity and General Conic
Comprehensive Exam Strategy (Q&A)
Related Revision Notes
Conclusion
📚 Related Topics

Conic Sections Class 11 Mathematics Revision — JEE 2026 Grandmaster Guide

What is Conic Sections Revision Notes?

[!TIP] 🚀 2-Minute Quick Recall Summary (Save for Exam Day)

Circle: (x-h)² + (y-k)² = r². Center (h, k), radius r.

Parabola (y² = 4ax): Vertex (0,0), Focus (a, 0), Directrix x = -a.

Ellipse (x²/a² + y²/b² = 1): Focus (± eye, 0). Eccentricity e = √(1 - b²/a²) for a > b.

Hyperbola (x²/a² - y²/b² = 1): Focus (± eye, 0). Eccentricity e = √(1 + b²/a²).

Lotus Rectum Length:

Parabola: 4a.

Ellipse/Hyperbola: 2b²/a. 📥 Download 1-Page Short Notes PDF (Zero-Friction)

Introduction

1. The Circle

A circle is the set of all points and a plane that are at a constant distance (radius) from a fixed point (center).

Standard Equation (Center at (h, k)): (x - h)² + (y - k)² = r²
Simple Case (Center at (0, 0)): x² + y² = r²

2. The Parabola

A parabola is the set of all points and a plane that are equidistant from a fixed line (directrix) n a fixed point (focus).

Standard Form (y² = 4ax):

Vertex: (0, 0)
Focus: (a, 0)
Directrix: x = -a
Axis of Symmetry: y = 0
Length of Lotus Rectum: 4a

3. The Ellipse

An ellipse is the set of all points and a plane, the $\sum of whose distances from two fixed points (foci) is a constant.$

Standard Form (x²/a² + y²/b² = 1, where a > b):

Center: (0, 0)
Vertices: (± a, 0)
Foci: (±c, 0) where c² = a² - b².
Eccentricity (e): e = c/a = √(1 - b²/a²). (Note: 0 < e < 1).
Length of Lotus Rectum: 2b²/a.

4. The Hyperbola

A hyperbola is the set of all points and a plane, the difference of whose distances from two fixed points (foci) is a constant.

Standard Form (x²/a² - y²/b² = 1):

Center: (0, 0)
Vertices: (± a, 0)
Foci: (±c, 0) where c² = a² + b².
Eccentricity (e): e = c/a = √(1 + b²/a²). (Note: e > 1).
Length of Lotus Rectum: 2b²/a.

5. Eccentricity and General Conic

The eccentricity e is the ratio of the distance from the focus to the distance from the directrix.

Circle: e = 0
Parabola: e = 1
Ellipse: 0 < e < 1
Hyperbola: e > 1

Comprehensive Exam Strategy (Q&A)

Q1: Find the equation of the circle with center (2, -3) n radius 5. Answer:

(x - 2)² + (y - (-3))² = 5²
(x - 2)² + (y + 3)² = 25
x² - 4x + 4 + y² + 6y + 9 = 25 => x² + y² - 4x + 6y - 12 = 0. Q2: Find the focus and the length of the lotus rectum for the parabola y² = 12x. Answer:
Comparing with y² = 4ax: 4a = 12 => a = 3.
Focus = (a, 0) = (3, 0).
Length of Lotus Rectum = 4a = 12. Q3: Find the eccentricity of the ellipse 4x² + 9y² = 36. Answer:
Divide y 36: x²/9 + y²/4 = 1.
Here a² = 9, b² = 4 => a = 3, b = 2.
e = √(1 - b²/a²) = √(1–4/9) = √(5/9)
e = √5 / 3.

Related Revision Notes

Chapter 10: Straight Lines
Chapter 12: Three Dimensional Geometry
[External Reference: CERT Class 11 Math Chapter 11 (Authoritative Source)]

Conclusion

📚 Related Topics

Continue your revision with these related guides:

🚀 Ready to Ace Your Exam?

Put your knowledge to the test! Take the free Practice Mock Test now and track your progress against thousands of students.

📚 Related Topics

Continue your revision with these related guides:

🪤 The 5 Mistakes That Cost Marks

Confusing the equation of a circle with the equation of a parabola: A common mistake is writing the equation of a circle as y^2 = 4ax $instead of$ (x-h)^2 + (y-k)^2 = r^2 $, which can lead to incorrect solutions.$
Forgetting to check the axis of a parabola: When dealing with a parabola, it's crucial to identify whether the axis is along the x-axis or the y-axis, as this affects the equation and subsequent calculations.
Mixing up the formulas for ellipse and hyperbola: The equations for ellipses and hyperbolas can be similar, but using the wrong formula can result and incorrect solutions, so it's essential to double-check the equation.
Not considering the domain and range when dealing with conic sections: When solving problems involving conic sections, it's vital to consider the domain and range of the functions to avoid extraneous solutions.
Incorrectly identifying the center and vertices of conic sections: Incorrectly identifying the center and vertices of conic sections can lead to errors and subsequent calculations, so it's crucial to carefully identify these key points.

🔁 Last 5 Minutes Box

Circle: $(x-h)^2 + (y-k)^2 = r^2$ $(x - h)^{2} + (y - k)^{2} = r^{2}$ , center $(h, k)$ $(h, k)$ , radius are
- Parabola: y^2 = 4ax $, focus$ (a, 0) $, directrix x = -a$
- Ellipse: $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ , foci $(pm eye, 0)$ , he = $\sqrt{1 -\frac{b^2}{a^2}}$
- Hyperbola: $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$ , foci $(pm eye, 0)$ , he = $\sqrt{1 +\frac{b^2}{a^2}}$
- Eccentricity: = \f{c}{a} $, where is distance from center to focus$
- Equation of tangent to circle: - y_1 = m(x - x_1) $, where is slope$
- Polar equation of conic: = \f{l}{1 + e } $, where is distance from focus to directrix$