Chapter 13 of 42
Revision Notes
Pair of Straight Lines — Revision Notes
JEE Mains · Mathematics
Free Pair of Straight Lines revision notes for JEE Mains Mathematics 2026 — key concepts, formulas, and definitions for quick revision.
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Key concepts, formulas, and definitions from Pair of Straight Lines for JEE Mains Mathematics preparation.
Key Topics to Revise
1
Joint Equation of Pair of Straight Lines
- If two lines have equations L₁ = a₁x + b₁y + c₁ = 0 and L₂ = a₂x + b₂y + c₂ = 0, their joint equation is (a₁x + b₁y + c₁)(a₂x + b₂y + c₂) = 0
- The joint equation is always a quadratic equation in x and y
- To find component lines from joint equation, factorize the quadratic expression
2
General Second Degree Equation and Condition for Pair of Lines
- General form: ax² + 2hxy + by² + 2gx + 2fy + c = 0
- Condition for representing pair of lines: abc + 2fgh - af² - bg² - ch² = 0
- This condition can be written as a determinant equaling zero
3
Point of Intersection of Pair of Lines
- Direct formula: Point of intersection = ((bg-hf)/(h²-ab), (af-gh)/(h²-ab))
- Alternative method: Use partial derivatives to find intersection point
- Elementary method: Find component lines and solve simultaneously
4
Homogeneous Second Degree Equations
- Form: ax² + 2hxy + by² = 0 represents pair of lines through origin
- Condition for real and distinct lines: h² > ab
- If lines have slopes m₁ and m₂, then m₁ + m₂ = -2h/b and m₁m₂ = a/b
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Key Concepts
If L₁ = a₁x + b₁yThe general form ax² + 2hxyFor the equation ax² + 2hxyEquations of the form ax² +For lines represented by ax² +
Frequently Asked Questions
What topics are covered in Pair of Straight Lines for JEE Mains?
Pair of Straight Lines is an important chapter in JEE Mains Mathematics. It covers key concepts and formulas that are frequently tested in the exam. Key topics include: Joint Equation of Pair of Straight Lines, General Second Degree Equation and Condition for Pair of Lines, Point of Intersection of Pair of Lines, Homogeneous Second Degree Equations.
How important is Pair of Straight Lines for JEE Mains?
Pair of Straight Lines is a frequently tested chapter in JEE Mains Mathematics. Questions from this chapter appear regularly in previous year papers. There are 47 practice questions available for this chapter.
How to prepare Pair of Straight Lines 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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