Definition:One-Parameter Family of Curves

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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.


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