Question

How do you convert `x² + (y + 4)² = 16` to polar form?

Answer 1

`r^2+8rsintheta=0`

Explanation:

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

Therefore ## can be written as

`(rcostheta)^2+(rsintheta+4)^2=16`

or `r^2cos^2theta+r^2sin^2theta+8rsintheta+16=16`

or `r^2(cos^2theta+sin^2theta)+8rsintheta=0`

or `r^2+8rsintheta=0`