# How to graph curves that are not functions

## Description

Assume we have an equation in which $y$ cannot be isolated as a function of $x$. (The standard example is the formula for the unit circle, $x^2+y^2=1$.) We would still like to be able to use software to plot such curves. How?

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## Using SymPy, in Python

This answer assumes you have imported SymPy as follows.

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from sympy import * # load all math functions
init_printing( use_latex='mathjax' ) # use pretty math output

Let’s consider the example of the unit circle, $x^2+y^2=1$.

To plot it, SymPy first expects us to move everything to the left-hand side of the equation, so in this case, we would have $x^2+y^2-1=0$.

We then use that left hand side to represent the equation as a single formula,
and we can plot it with SymPy’s `plot_implicit`

function.

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var( 'x y' )
formula = x**2 + y**2 - 1 # to represent x^2+y^2=1
plot_implicit( formula )

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<sympy.plotting.plot.Plot at 0x7f67130cb460>

Content last modified on 24 July 2023.

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