How do you convert the polar equation #r=3/(1-sintheta)# into rectangular form?

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Answer 1 · 2017-02-02T07:40:19

The answer is #y=(x^2-9)/6#

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

#x=rcostheta#

#y=rsin theta#

#x^2+y^2=r^2#

Therefore,

#r=3/(1-sintheta)#

#r(1-sintheta)=3#

#r-rsintheta=3#

#r=3+rsintheta#

#sqrt(x^2+y^2)=3+y#

#x^2+y^2=(3+y)^2=9+6y+y^2#

#x^2=9+6y#

#6y=x^2-9#

#y=(x^2-9)/6#