![cover image](https://wikiwandv2-19431.kxcdn.com/_next/image?url=https://upload.wikimedia.org/wikipedia/commons/thumb/b/b2/Apollonian_circles.svg/640px-Apollonian_circles.svg.png&w=640&q=50)
Family of curves
Set of curves from a function with variable parameter(s) / From Wikipedia, the free encyclopedia
In geometry, 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.
![Thumb image](http://upload.wikimedia.org/wikipedia/commons/thumb/b/b2/Apollonian_circles.svg/320px-Apollonian_circles.svg.png)
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when an additive constant of integration is introduced, it will usually be manipulated algebraically until it no longer represents a simple linear transformation.
Families of curves may also arise in other areas. For example, all non-degenerate conic sections can be represented using a single polar equation with one parameter, the eccentricity of the curve:
as the value of e changes, the appearance of the curve varies in a relatively complicated way.