User:AMMAR-DMOUR/Family of curves

A family of curves is a set of curves, each of which is given by a function or parametrization in which one or more of the parameters is variable. In general, the parameter(s) influence the shape of the curve in a way that is more complicated than a simple linear transformation. Sets of curves given by an implicit relation may also represent families of curves.

Families of curves appear frequently in solutions of differential equations; when an additive constant of integration is introduced, it will usually be manipulated algebraically until it no longer represents a simple linear transformation