How do I convert 2r=tan(theta) into a rectangular equation?

1 Answer
Apr 16, 2018

#4x^2(x^2+y^2)=y^2#

Explanation:

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

#x=rcostheta#, #y=rsintheta# which give us #x^2+y^2=r^2# and #tantheta=y/x#

Hence we can write #2r=tantheta# as

#2sqrt(x^2+y^2)=y/x#

or #4(x^2+y^2)=y^2/x^2#

or #4x^2(x^2+y^2)=y^2#