What the is the polar form of #2 = -x-5x^2y-x/y +y^2 #?

1 Answer
Shwetank Mauria
Oct 15, 2017

#5r^3sinthetacos^2theta-r^2sin^2theta+rcostheta+2+cottheta=0#

Explanation:

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

#x=rcostheta# and #y=rsintheta#

Hence, #2=-x-5x^2y-x/y+y^2# can be written as

#2=-rcostheta-5r^2cos^2thetarsintheta-(rcostheta)/(rsintheta)+r^2sin^2theta#

or #2=-rcostheta-5r^3sinthetacos^2theta-cottheta+r^2sin^2theta#

or #5r^3sinthetacos^2theta-r^2sin^2theta+rcostheta+2+cottheta=0#

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