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6.Parabola, Ellipse & Hyperbola (Intro)
Class 11 • Mathematics • NCERT
Parabola, Ellipse & Hyperbola (Introduction)
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This lesson introduces parabola, ellipse, and hyperbola using the focus–directrix definition as per NCERT Class 11. Students learn how conic sections are classified using eccentricity with strong conceptual clarity.
Lesson Objectives
- Understand the focus–directrix definition.
- Learn what eccentricity means.
- Differentiate between parabola, ellipse, and hyperbola.
- Build a strong foundation for conic sections.
1. What Are Conic Sections?
Conic sections are curves obtained by cutting a cone with a plane.
The main conic sections studied in Class 11 are:
• Circle
• Parabola
• Ellipse
• Hyperbola
• Circle
• Parabola
• Ellipse
• Hyperbola
2. Focus–Directrix Definition
A conic section is the locus of a point whose distance from a fixed point bears a constant ratio to its distance from a fixed line.
• Fixed point → Focus
• Fixed line → Directrix
• Constant ratio → Eccentricity (e)
• Fixed line → Directrix
• Constant ratio → Eccentricity (e)
3. Eccentricity
The constant ratio of distances is called eccentricity.
e = (Distance from focus) / (Distance from directrix)
4. Types of Conic Sections
• Parabola → e = 1
• Ellipse → e < 1
• Hyperbola → e > 1
• Circle → e = 0
• Ellipse → e < 1
• Hyperbola → e > 1
• Circle → e = 0
5. Geometrical Meaning (NCERT Insight)
Different values of eccentricity change the shape of the curve.
• Smaller e → curve closer to circle
• Larger e → curve more open
• Parabola lies between ellipse and hyperbola
• Larger e → curve more open
• Parabola lies between ellipse and hyperbola
Practice Questions (NCERT)
- What are conic sections?
- Define focus and directrix.
- What is eccentricity?
- What is the value of eccentricity for a parabola?
- Which conic has eccentricity less than 1?
- Which conic has eccentricity greater than 1?
- What is the eccentricity of a circle?
- Which conic lies between ellipse and hyperbola?
- What determines the shape of a conic?
- Is this topic part of NCERT Class 11 syllabus?
✅ Show Answer Key
- Curves obtained by cutting a cone with a plane.
- Fixed point and fixed line used in definition.
- Ratio of distances from focus and directrix.
- 1
- Ellipse
- Hyperbola
- 0
- Parabola
- Eccentricity
- Yes
© Aviate Learning – Conic Sections (NCERT Class 11)