Plotting Implicit Functions

## Description

An implicit equation is a relation which can be defined as $R(x_0, x_1, \ldots, x_n)=0$, where R is usually a function of several variables. An implicit function occurs if we consider one of the variables to depend on the remaining variables. One example of an implicit function is the circle of radius 1 centered at the origin, which is defined as

(1)
$$x^2+y^2-1=0.$$

We consider $y$ to be an implicitly defined function of $x$. The Sage cell below plots the implicit function.

## Sage Cell

#### Code

g(x,y) = x^2 + y^2-1
g_plot=implicit_plot(g, (x,-1,1), (y,-1,1), frame=True, gridlines=True )
g_plot


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## Tags

Primary Tags: Plotting: Two-dimensional plots.

Secondary Tags: Two-dimensional plots: Implicit plots.

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