How do you convert #5y=(x+y)^2 -2xy # into a polar equation?

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Answer 1 · 2018-03-15T05:41:39

#r=5sintheta#

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

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

Therefore we can write #5y=(x+y)^2-2xy# as

#5rsintheta=x^2+y^2+2xy-2xy#

or #5rsintheta=x^2+y^2#

or #5rsintheta=r^2#

or #r=5sintheta#

This is the equation of a circle

graph{5y=(x+y)^2-2xy [-10.13, 9.87, -2.92, 7.08]}