Question 1131216: Convert the polar equation to rectangular coordinates. (Use variables x and y as needed.)
r = −3
Found 4 solutions by MathLover1, ikleyn, MathTherapy, greenestamps:
Answer by MathLover1(20850)   (Show Source):
Answer by ikleyn(52898)  (Show Source):
You can put this solution on YOUR website! .
Convert the polar equation to rectangular coordinates. (Use variables x and y as needed.)
r = −3
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Traditionally, in polar coordinates, the variable " r " is the distance from the origin in a coordinate plane.
In polar coordinates, the radius r should be non-negative to describe non-empty set of points.
In your case, with r negative r= -3, it describes EMPTY set of points.
The answer by @MathLover1 is incorrect.
Answer by MathTherapy(10557)  (Show Source):
You can put this solution on YOUR website! Convert the polar equation to rectangular coordinates. (Use variables x and y as needed.)
r = −3
"r" CANNOT be negative, so IGNORE the person who claims that it can be.
It can be 0, but not < 0. In other words, 
Answer by greenestamps(13214)  (Show Source):
You can put this solution on YOUR website!
I will disagree with tutors @MathTherapy and @ikleyn, both of whom say the solution is the empty set and the solution by tutor @MathLover1 is incorrect.
In polar coordinates, r can be negative. (-3,pi/2) is a valid description of a point in polar coordinates; so it is a point on the graph of r=-3.
Any point with polar coordinates (3,theta) can be represented also by (-3,theta+pi); or with an infinite number of other representations with r equal to either 3 or -3. So the graph of r=-3 is the same as the graph of r=3.
If it were the case that r can't be negative, then simple polar equations like r=sin(theta) or r = -2+cos(theta) would be invalid.
The equation r=-3 is independent of the angle theta; it is equivalent to the equation r=3. Both equations are of a circle with center at the origin and radius 3.
As tutor @MathLover1 said, the equation in rectangular coordinates is
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