Parabola — Revision Notes
JEE Advanced · Mathematics
Quick revision notes for Parabola — key concepts, formulas, and definitions for JEE Advanced Mathematics preparation.
Revision Notes — Parabola
Key concepts, formulas, and definitions from Parabola for JEE Advanced Mathematics preparation.
Key Topics to Revise
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
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
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
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
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What topics are covered in Parabola for JEE Advanced?
Parabola is an important chapter in JEE Advanced 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 Advanced?
Parabola is a frequently tested chapter in JEE Advanced Mathematics. Questions from this chapter appear regularly in previous year papers. There are 69 practice questions available for this chapter.
How to prepare Parabola for JEE Advanced?
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.