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

\begin{equation} x^2+y^2-1=0. \end{equation}

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
```

## Options

None

## Tags

Primary Tags: Plotting: Two-dimensional plots.

Secondary Tags: Two-dimensional plots: Implicit plots.

## Related Cells

## Attribute

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Date: 30 Oct 2018 20:21

Submitted by: James A Phillips