How do you convert #x^2 + y^2 = 4x + 4y# to polar form?

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How do you convert #x^2 + y^2 = 4x + 4y# to polar form?

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Answer 1 · 2016-10-15T20:10:12

#r=4costheta+4sintheta#

Explanation:

#x=rcostheta#
#y=rsintheta#
#LHS=x^2+y^2=r^2cos^2theta+r^2sin^2theta=r^2(cos^2theta+sin^2theta)=r^2#
As #cos^2theta+sin^2theta=1#
#RHS=4rcostheta+4rsintheta=4r(cos theta+sintheta)#
LHS=RHS
#r^2=4r(costheta+sintheta)#
Finally #r=4(costheta+sintheta)#

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How do you convert #x^2 + y^2 = 4x + 4y# to polar form?

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