How do you change the polar equation #r+5sintheta=0# into rectangular form?

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Answer 1 · 2016-10-27T17:42:44

#x^2+y^2+5y=0#

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

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

Hence #r+5sintheta=0#

#hArrr×r+5×r×sintheta=0#

or #r^2+5×rsintheta=0#

or #x^2+y^2+5×y=0#

i.e. #x^2+y^2+5y=0#