How do you convert #2=(2x+6y)^2-y-3x# into polar form?

1 Answer
Shwetank Mauria
Oct 7, 2016

Pola fom is #4r^2(1+8sin^2theta+6sinthetacostheta)-r(sintheta+3costheta)-2=0#

Explanation:

The relation between polar coordinates #(r,theta)# and Cartesian coordinates #(x,y)# is #x=rcostheta# and #y=rsintheta#.

Therefore #2=(2x+6y)^2-y-3x# can be written as

#2=(2rcostheta+6rsintheta)^2-rsintheta-3rcostheta#

or #2=r^2(4cos^2theta+36sin^2theta+24sinthetacostheta)-r(sintheta+3costheta)#

or #2=r^2(4+32sin^2theta+24sinthetacostheta)-r(sintheta+3costheta)#

or #4r^2(1+8sin^2theta+6sinthetacostheta)-r(sintheta+3costheta)-2=0#

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