How do you convert the polar equation #r=6/(2costheta-3sintheta)# into rectangular form?

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Answer 1 · 2017-01-22T09:51:52

The equation is #y=2/3x-2#

To convert from polar coordinates #(r, theta)# to rectangular coordinates #(x,y)#, we use the equations

#x=rcostheta#

#y=rsintheta#

Let's rewrite the equation

#r=6/(2costheta-3sintheta)#

#r(2costheta-3sintheta)=6#

#2rcostheta-3rsintheta=6#

Therefore,

#2x-3y=6#

#3y=2x-6#

#y=2/3x-2#

This is the equation of a line