Chapter 23 of 42
Important Topics
Parabola — Important Topics
JEE Mains · Mathematics
Most important topics from Parabola for JEE Mains Mathematics. Focus on these high-weightage areas for maximum score.
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Get startedParabola — Syllabus & Topics
Topics covered in Parabola for JEE Mains Mathematics.
Topics in Parabola
1
Definition and Basic Properties
- A parabola is the locus of a point P such that its distance from a fixed point S (focus) equals its distance from a fixed line l (directrix)
- The eccentricity of a parabola is always 1 (e = 1)
- The axis of symmetry passes through the focus and is perpendicular to the directrix
2
Standard Forms and Equations
- Four standard forms based on axis orientation and opening direction
- For y² = 4ax: vertex at origin, opens rightward, focus at (a,0), directrix x = -a
- For y² = -4ax: vertex at origin, opens leftward, focus at (-a,0), directrix x = a
3
Shifted Parabolas and General Forms
- When vertex is at (h,k), replace x with (x-h) and y with (y-k) in standard equation
- General form: (y-k)² = 4a(x-h) for horizontal axis
- General form: (x-h)² = 4a(y-k) for vertical axis
4
Focal Chord Properties and Applications
- Focal chord passes through the focus of the parabola
- For parabola y² = 4ax, if focal chord has endpoints with parameters t₁ and t₂, then t₁t₂ = -1
- Length of focal chord with endpoints P(t₁) and Q(t₂) is a(t₁ + 1/t₁)²
Key Concepts
A parabola is the locusFour standard forms existAny point on parabola y² =Parabolas with vertex at (hA focal chord passes through
Frequently Asked Questions
What topics are covered in Parabola for JEE Mains?
Parabola 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, Standard Forms and Equations, Shifted Parabolas and General Forms, Focal Chord Properties and Applications.
How important is Parabola for JEE Mains?
Parabola is a frequently tested chapter in JEE Mains Mathematics. Questions from this chapter appear regularly in previous year papers. There are 71 practice questions available for this chapter.
How to prepare Parabola 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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