Pencil of Lines
The set of all lines in the same plane that pass through a given point called the centre of the pencil.
Examples
- Pencil of lines with its centre at the point with coordinates (3, 2) :
- In a Cartesian plane, a pencil of lines passing through a point with coordinates (p, q) is a family defined by the equation [latex]y\space =\space \dfrac{q−b}{p}x + b[/latex], where b is the y-intercept of each line in the pencil of lines.