How do you graph #r=-3#?

1 Answer
A. S. Adikesavan
Sep 9, 2016

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. .

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