Question

How do you convert `2=(8x+y)^2+2y` into polar form?

Answer 1

The equation is `r^2(8costheta+sintheta)^2+2rsintheta=2`

Explanation:

To convert from rectangular coordinates `(x,y)` to polar coordinates `(r, theta)`, apply the following

`{(x=rcostheta),(y=rsintheta),(x^2+y^2=r^2):}`

The equation

`2=(8x+y)^2+2y`

`(8rcostheta+rsintheta)^2+2rsintheta=2`

`r^2(8costheta+sintheta)^2+2rsintheta=2`

graph{((8x+y)^2+2y-2)=0 [-4.136, 6.96, -2.96, 2.59]}