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

1 Answer
May 20, 2018

color(blue)[r^2=(-costheta)/[sin^3theta-r^2*sin^3theta*cos^2theta-r^2costheta*sin^4theta]]

Explanation:

Note that

color(red)[y=r*sintheta]

color(red)[x=r*costheta]

y = x^2y-x/y^2 +xy^2

(r*sintheta)=(r*costheta)^2*(r*sintheta)-(r*costheta)/(r*sintheta)^2+(r*costheta)(r*sintheta)^2

rsintheta=r^3sintheta*cos^2theta-(costheta)/(rsin^2theta)+r^3costheta*sin^2theta

[rsintheta-r^3sintheta*cos^2theta-r^3costheta*sin^2theta]/1=-(costheta)/(rsin^2theta)

r^2sin^3theta-r^4*sin^3theta*cos^2theta-r^4costheta*sin^4theta=-costheta

color(blue)[r^2=(-costheta)/[sin^3theta-r^2*sin^3theta*cos^2theta-r^2costheta*sin^4theta]]