Allowing that r could be negative (against the befitting definition that as length (modulus ) of a vector ##r>=0) r =-3## represents the circle with center at the pole r = 0 and radius = 3..

Despite that r is understood as length (modulus ) of the position

vector from pole to the position ##(r theta)## it is customary to allow r

to be negative by identifying the point ##(+r theta)## as

##( -r theta+pi)##.

So both ##r=3## here and r=-3 represent the same circle with center

at the pole r = 0 and radius = 3.

The point ##(3 theta)## on the circle from the first equation is (-3

theta+pi) from the second. .