What the is the polar form of x^2-y^2 = 6x-x^2y-y ?

1 Answer
Nov 30, 2017

r^2cos^2thetasintheta+rcos2theta+sintheta-6costheta=0

Explanation:

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

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

Hence we can write x^2-y^2=6x-x^2y-y as

r^2cos^2theta-r^2sin^2theta=6rcostheta-r^3cos^2thetasintheta-rsintheta

or r^3cos^2thetasintheta+r^2cos2theta+r(sintheta-6costheta)=0

or r^2cos^2thetasintheta+rcos2theta+sintheta-6costheta=0