Question

Test for symmetry with respect to θ = π/2, the polar axis, and the pole.

r^2 = 36 cos 2θ

Answer 1

Step 1:

The polar equation is .

(i)

Test for Symmetry about the :

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 .

Step 2:

(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.

Step 3:

(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.

Solution:

The polar equation is is symmetric with respect to , polar axis and pole.