Conic Sections – Class 11 Maths (NCERT Based)
The chapter Conic Sections introduces curves obtained by cutting a right circular cone with a plane. It is an important part of coordinate geometry and has applications in physics, astronomy, and engineering.
This content strictly follows the NCERT Class 11 Maths syllabus and explains concepts in a clear, student-friendly manner.
📖 Definition of Conic Sections
A conic section is the curve obtained by intersecting a plane with a double-napped cone.
Depending on the angle of the plane, we get different curves:
- Circle – plane perpendicular to cone axis
- Ellipse – plane angled but not parallel to base
- Parabola – plane parallel to one slant of cone
- Hyperbola – plane cuts both nappes
🔹 Circle
Equation of a circle with center (h, k) and radius r:
(x − h)² + (y − k)² = r²
- Center: (h, k)
- Radius: r
Special Case: Circle at origin → x² + y² = r²
🔹 Parabola
Equation of a parabola with vertex at origin:
- Opens upwards/downwards: y² = 4ax
- Opens sideways: x² = 4ay
- Focus: Point that defines parabola
- Directrix: Line equidistant from vertex, used with focus
🔹 Ellipse
Equation of an ellipse with center at origin:
(x² / a²) + (y² / b²) = 1, a > b
- Major axis: 2a
- Minor axis: 2b
- Foci: (±√(a² − b²), 0)
Special Case: Circle → a = b
🔹 Hyperbola
Equation of a hyperbola with center at origin:
- Horizontal hyperbola: x² / a² − y² / b² = 1
- Vertical hyperbola: y² / a² − x² / b² = 1
- Foci: (±√(a² + b²), 0)
- Asymptotes: y = ±(b/a)x