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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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