Pencil of Lines

Pencil of Lines

The set of all lines in the same plane that pass through a given point called the centre of the pencil.


  • Pencil of lines with its centre at the point with coordinates (3, 2) :

Faisceau droites

  • In a Cartesian plane, a pencil of lines passing through a point with coordinates (pq) is a family defined by the equation \(y\space =\space \dfrac{q−b}{p}x + b\), where b is the y-intercept of each line in the pencil of lines.


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