document.write( "Question 1131216: Convert the polar equation to rectangular coordinates. (Use variables x and y as needed.)
\n" ); document.write( "r = −3 \n" ); document.write( "

Algebra.Com's Answer #747880 by greenestamps(13203) $\"\"$ $\"About$

You can put this solution on YOUR website!

\n" ); document.write( "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.

\n" ); document.write( "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.

\n" ); document.write( "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.

\n" ); document.write( "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.

\n" ); document.write( "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.

\n" ); document.write( "As tutor @MathLover1 said, the equation in rectangular coordinates is

\n" ); document.write( " $\"x%5E2%2By%5E2=9\"$ \n" ); document.write( "

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