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A pencil is a one-parameter linear family of geometric objects. For linearly independent homogeneous polynomials $F,G$ of equal degree, $sF+tG=0$, indexed by $[s:t]\in {\mathbb{P}}^1$, 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.

Given homogeneous polynomials $F,G$ of the same degree, their pencil is the one-parameter familyIts total space is the projective hypersurface $V(sF+tG)\subseteq {\mathbb{P}}^2\times {\mathbb{P}}^1$, and projection to $[s:t]$ has these plane curves as its fibres.

It is a pencil whose members are plane curves.