Question

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

Answer 1

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`