Convert the polar equations to a rectangular equations?!

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Answer 1 · 2018-05-14T08:40:08

C. #36x^2+27y^2-24y-16=0#

Multiply both sides by #6csctheta-3# to get:
#r(6csctheta-3)=4csctheta#

Then multiply each side by #sintheta# to cancel out the #csctheta#

#6r-3rsintheta=4#

#r=sqrt(x^2+y^2)#
#rsintheta=y#

#6sqrt(x^2+y^2)-3y=4#

#6sqrt(x^2+y^2)=4+3y#

#36(x^2+y^2)=(4+3y)^2#

#36x^2+36y^2=16+24y+9y^2#

#36x^2+36y^2-16-24y-9y^2=0#

#36x^2+27y^2-24y-16=0# which is the same as C