Definition:One-Parameter Family of Curves

From ProofWiki
Jump to navigation Jump to search

Definition

Consider the implicit function $\map f {x, y, c} = 0$ in the $\tuple {x, y}$-plane where $c$ is a constant.


For each value of $c$, we have that $\map f {x, y, c} = 0$ defines a relation between $x$ and $y$ which can be graphed in the cartesian plane.

Thus, each value of $c$ defines a particular curve.


The complete set of all these curve for each value of $c$ is called a one-parameter family of curves.


Parameter

The value $c$ is the parameter of $F$.


Sources