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Conic Sections — Revision Notes

IISER Aptitude Test · Mathematics

Free Conic Sections revision notes for IISER Aptitude Test Mathematics 2026 — key concepts, formulas, and definitions for quick revision.

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A 3D diagram illustrating how different conic sections (circle, ellipse, parabola, hyperbola) are formed by the intersection of a plane with a double-napped right circular cone at various angles.
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Revision Notes — Conic Sections

Key concepts, formulas, and definitions from Conic Sections for IISER Aptitude Test Mathematics preparation.

Key Topics to Revise

1

Introduction to Conic Sections

  • A conic is the locus of a point whose ratio of distances from a fixed point (focus) to a fixed line (directrix) is constant (eccentricity)
  • General equation of second degree: Ax² + 2Hxy + By² + 2Gx + 2Fy + C = 0
  • Classification based on eccentricity: Circle (e=0), Parabola (e=1), Ellipse (e<1), Hyperbola (e>1)
2

Circle

  • Locus of points equidistant from a fixed point (center)
  • Standard form: (x-h)² + (y-k)² = r² where (h,k) is center and r is radius
  • General form: x² + y² + 2gx + 2fy + c = 0
3

Parabola

  • Locus of points equidistant from focus and directrix (eccentricity = 1)
  • Four standard forms based on orientation: y² = 4ax, y² = -4ax, x² = 4ay, x² = -4ay
  • Focus and directrix are equidistant from vertex
4

Ellipse

  • Locus where sum of distances from two foci is constant (eccentricity < 1)
  • Standard forms: x²/a² + y²/b² = 1 (horizontal major axis when a > b)
  • Major axis length = 2a, minor axis length = 2b

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Key Concepts

A conic section is the locusStandard formFour standard forms based on orientationStandard formsStandard hyperbola

Frequently Asked Questions

What topics are covered in Conic Sections for IISER Aptitude Test?
Conic Sections is an important chapter in IISER Aptitude Test Mathematics. It covers key concepts and formulas that are frequently tested in the exam. Key topics include: Introduction to Conic Sections, Circle, Parabola, Ellipse.
How important is Conic Sections for IISER Aptitude Test?
Conic Sections is a frequently tested chapter in IISER Aptitude Test Mathematics. Questions from this chapter appear regularly in previous year papers. There are 820 practice questions available for this chapter.
How to prepare Conic Sections for IISER Aptitude Test?
Start by understanding the core concepts, then solve practice questions. Focus on formulas and their applications. Use revision notes for quick review before the exam.

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