Implicit curve

In mathematics an implicit curve is a plane curve which is defined by an equation

Hence an implicit curve can be considered as the set of zeros of a function of two variables. Implicit means that the equation is not solved for either x or y.

If ${\displaystyle F(x,y)}$ is a polynomial in two variables, the corresponding curve is called an algebraic curve, and specific methods are available for studying it.

The graph of a function is usually described by an equation ${\displaystyle y=f(x)}$ and is called an explicit representation. The third essential description of a curve is the parametric one: (x(t), y(t)), where the x- and y-coordinates of curve points are represented by two functions ${\displaystyle x(t)\,,y(t)}$ dependent on a common parameter ${\displaystyle t.}$ The change of representations is unusually simple only when the explicit representation ${\displaystyle y=f(x)}$ is given: ${\displaystyle y-f(x)=0}$ (implicit), ${\displaystyle (t,f(t))}$ (parametric).

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