Class 11 Maths Chapter 10 Conic Sections – Revision Notes

Conic sections get their name from the way each curve is produced by cutting a cone at a particular angle. Chapter 10 of Class 11 Maths lists the standard equation and defining property of the circle, parabola, ellipse, and hyperbola.

Last Updated: September 23, 2026

Types

• Circle: perpendicular plane cut.
• Ellipse: angled plane cut (not parallel to edge).
• Parabola: plane parallel to slant edge.
• Hyperbola: plane cuts both nappes.

Standard Equations

• Circle (centre h,k): (x−h)²+(y−k)²=r².
• Parabola: y²=4ax.
• Ellipse: x²/a²+y²/b²=1.
• Hyperbola: x²/a²−y²/b²=1.

Key Definitions

• Parabola: equidistant from focus & directrix.
• Ellipse: sum of distances to 2 foci = constant.
• Hyperbola: |difference| of distances to 2 foci = constant.

One-Line Summary

Conic sections (circle, parabola, ellipse, hyperbola) arise from slicing a cone at different angles, each with a standard equation and a defining distance property relating to focus/foci.

Quick visual: a worked diagram from the full Solutions page, for reference.

Frequently Asked Questions

Why are circle, parabola, ellipse, and hyperbola grouped together as conic sections?
All four curves are obtained by intersecting a plane with a double-napped right circular cone at different angles, which is why they share a common family of equations and properties.

What determines whether a conic is a circle, ellipse, parabola, or hyperbola?
It depends on the eccentricity. A circle has eccentricity 0, an ellipse has eccentricity between 0 and 1, a parabola has eccentricity exactly 1, and a hyperbola has eccentricity greater than 1.

Written by Satish

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