How do we write the polar equation #r=3tantheta# in Cartesian coordinates?

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Answer 1 · 2017-07-18T08:53:41

#9y^2=x^4+x^2y^2#

we need the conversion formulae

#r^2=x^2+y^2--(1)#

#x=rcostheta---(2)#

#y=rsintheta---(3)#

we have

#color(red)(r=3tantheta)#

we have #tantheta# so #(3)-:(2)#

#y/x=(cancel(r)sintheta)/(cancel(r)costheta)=tantheta---(4)#

from #(1)" "#we have #" "r=sqrt(x^2+y^2)---(5)#

#(4)" "(5)" "#into the original equation

#color(red)(sqrt(x^2+y^2)=3y/x#

square both sides

#x^2+y^2=(9y^2)/x^2#

#:.9y^2=x^4+x^2y^2#