If (r,-θ), then r=16 cos 2(-θ)= 16 cos 2θ...... (as cos is an even fun).
If (-r,-θ) ⇒ -r=16 cos 2(-θ) =16 cos 2θ
r= -16 cos 2θ
If (-r,θ) ⇒ -r= 16 cos 2θ
r = -16 cos 2θ
symmetry with respect to origin .....no
Draw graph ,check answer that it satisfies.
Sometimes it is best to look at the graph of the polar function instead of trusting algebraic manipulation.
Meena from Strongsville , OH