How do you convert #9=(x-7)^2+(y+7)^2# into polar form?

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Answer 1 · 2017-07-15T17:18:42

#r^2-14r(sintheta-costheta)+89=0#

or #r^2-14sqrt2rsin(theta-pi/4)+89=0#

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

#x=rcostheta#, #y=rsintheta# i.e. #x^2+y^2=r^2#

Hence we can write #9=(x-7)^2+(y+7)^2# as

#(rcostheta-7)^2+(rsintheta+7)^2=9#

or #r^2cos^2theta-14rcostheta+49+r^2sin^2theta+14rsintheta+49=9#

or #r^2-14r(sintheta-costheta)+89=0#

or #r^2-14sqrt2rsin(theta-pi/4)+89=0#