Question

How do you graph `r=-3`?

Answer 1

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..

Explanation:

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. .