How do you convert the rectangular equation #y^2+(x-3)^2=9# into polar form?

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Answer 1 · 2016-10-04T09:13:48

#r=6costheta#

The relation between rectangular Cartesian coordinates #(x,y)# and polar coordinates #(r,theta)# is given by

#x=rcostheta#, #y=rsintheta# and #x^2+y^2=r^2#

Hence #y^2+(x-3)^2=9# can be rewritten as

#y^2+x^2+9-6x=9#

or #y^2+x^2-6x=0#

or #r^2-6rcostheta=0#

or #r^2=6rcostheta#

or #r=6costheta#