A pencil is a one-parameter linear family of geometric objects. For linearly independent homogeneous polynomials of equal degree, , indexed by , is a pencil of plane curves or hypersurfaces. Lines through a fixed point give a simple example; a pencil of plane curves specializes the general construction.
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In geometry, a "pencil" typically refers to a collection of geometric objects that share a common property, often associated with points or lines. The most common usage involves a "pencil of lines" or "pencil of rays." ### Pencil of Lines: A pencil of lines is a set of lines that all pass through a single point, known as the "vertex" or "center" of the pencil.