$\"\"$

The polar equation is $\"\"$ .

(i)

Test for Symmetry about $\"\"$ :

Replace $\"\"$ and simplify the equation.

If the resulting equation is equal to the original equation then it is

symmetry about $\"\"$ .

$\"\"$

The polar equation is symmetric with respect to $\"\"$ .

$\"\"$

(ii)

Test for Symmetry about polar-axis:

Replace $\"\"$ and simplify the equation.

If the resulting equation is equal to the original equation then it is

symmetry about polar axis.

$\"\"$

The polar equation is symmetric with respect to polar axis.

$\"\"$

(iii)

Test for Symmetry about pole:

Replace $\"\"$ and simplify the equation.

If the resulting equation is equal to the original equation then it is

symmetry about pole.

$\"\"$

The polar equation is symmetric with respect to pole.

$\"\"$

The polar equation is $\"\"$ is symmetric with respect to $\"\"$ ,

polar axis and pole.