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Rectangular equations that are not functions, such as equations representing ellipses or circles, are easier to graph in polar form.

Consider the circle equation in rectangular form $\"\"$ .

To graph such equations, represent the equations in the form of two equations.

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Hence graph the two functions : $\"\"$ and $\"\"$ .

Graph :

The eqaution of the circle corresponding to the rectangular form is $\"\"$ and $\"\"$ .

$\"\"$

The equation $\"\"$ can be written in polar form as $\"\"$ .

Graph:

The eqaution of the circle corresponding to the polar form is $\"\"$ .

$\"\"$

Observe the graph :

The equation $\"\"$ and $\"\"$ represent to be similar.

Hence the equations can be easily represented in polar form.

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Equations that represent functions, such as linear functions, are easier to graph in rectangular form.

Consider the line equation $\"\"$ .

Graph :

The eqaution of the circle corresponding to the rectangular form is $\"\"$ .

$\"\"$

The equation $\"\"$ can be written in polar form as $\"\"$ .

Graph:

The eqaution of the circle corresponding to the polar form is $\"\"$ .

$\"\"$

Observe the graph :

The equation $\"\"$ and $\"\"$ represent to be similar.

Hence the functions can be easily represented in rectangular form.

$\"\"$

The equations can be easily represented in polar form.

The functions can be easily represented in rectangular form.