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Syllabus

Ellipse — Syllabus

JEE Mains · Mathematics

Topics covered in Ellipse for JEE Mains Mathematics. Understand the syllabus structure and key areas to focus on.

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A diagram illustrating the definition of an ellipse as the locus of a point P such that its distance from a fixed point (focus S) divided by its distance from a fixed line (directrix L) is a constant
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Ellipse — Syllabus & Topics

Topics covered in Ellipse for JEE Mains Mathematics.

Topics in Ellipse

1

Definition and Basic Properties of Ellipse

  • An ellipse is the locus of a point such that the sum of its distances from two fixed points (foci) is constant
  • The ratio of distance from focus to distance from directrix is constant (eccentricity e), where 0 < e < 1
  • Major axis is the longest chord passing through both foci
2

Standard Forms of Ellipse

  • Case 1: Major axis along x-axis (a > b): x²/a² + y²/b² = 1
  • Case 2: Major axis along y-axis (a < b): x²/a² + y²/b² = 1
  • General form: (x-h)²/a² + (y-k)²/b² = 1 with center at (h,k)
3

Parametric Representation

  • Any point on ellipse x²/a² + y²/b² = 1 can be written as (a cos θ, b sin θ)
  • θ is called eccentric angle of the point
  • For ellipse with center (h,k): point is (h + a cos θ, k + b sin θ)
4

Tangent to Ellipse

  • Equation of tangent at point (x₁, y₁) on ellipse: xx₁/a² + yy₁/b² = 1
  • Tangent with slope m: y = mx ± √(a²m² + b²)
  • Condition for tangency: c² = a²m² + b² for line y = mx + c

Key Concepts

An ellipse is defined asTwo standard forms based on majorAny point on ellipse x²/a² +Tangent at point (x₁Normal at point (x₁

Frequently Asked Questions

What topics are covered in Ellipse for JEE Mains?
Ellipse is an important chapter in JEE Mains Mathematics. It covers key concepts and formulas that are frequently tested in the exam. Key topics include: Definition and Basic Properties of Ellipse, Standard Forms of Ellipse, Parametric Representation, Tangent to Ellipse.
How important is Ellipse for JEE Mains?
Ellipse is a frequently tested chapter in JEE Mains Mathematics. Questions from this chapter appear regularly in previous year papers. There are 68 practice questions available for this chapter.
How to prepare Ellipse for JEE Mains?
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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All 42 chapters — JEE Mains Mathematics Syllabus

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