# Pairs of Straight Lines

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#### Homogeneous Equation of Pair of Straight Lines

• Introduction
• Second Degree Homogenous Equation in x and y
• Theorems and proofs
• Nature of Line

#### Formation of Joint/Combined Equation of a pair of Lines – 01

• Type – IA: When Separate Equations are Given
• Type – IB: When angles Made by the Line With Coordinate Axes Given

#### Formation of Joint/Combined Equation of a pair of Lines – 02

• Type – IC: Lines Forming Equilateral Triangle With x = or y = K are Given
• Type – ID: When Slopes of Lines are Given
• Type – IE: When A Point and Lines Parallel to Coordinate axes are Given

#### Formation of Joint/Combined Equation of a pair of Lines – 03

• Type – IF: When a Point and Lines Parallel or Perpendicular to Given Lines are Given

#### Nature of Line

• Type – II A: To Find Nature of Line From Joint Equation
• Type – II B: To Find the Value of Constant Using Nature of Line

#### Separate Equations of Lines

• Type – III: To Find Separate Equations of Lines from Joint Equation

#### Condition That Joint Equation Represents a Pair of Lines

• Type – IV A: To Find Condition that Joint Equation Represents a Pair of Lines

#### To Find Constant if One of the Lines Represented by Joint Equation is Given

• Type IV B: Use of Auxiliary Equation of Line

#### To Find Constant When Relation Between Slopes is Given

• Type V: To Find Constant When Relation Between the Slopes is Given

#### Pair of Lines Perpendicular to Another Pair of Lines

• Type – VI: To Find Joint Equation of Pair of Lines Perpendicular To Lines Represented by Given Joint Equation.
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