Question

How do you convert `-2y+1=(x+4)^2+(y-1)^2` into polar form?

Answer 1

`r^2+8rcostheta+16=0`

Explanation:

`-2y+1=x^2+8x+16+y^2-2y+1`
`0=x^2+8x+16+y^2-2y+1+2y-1`
`0=x^2+8x+16+y^2`
`0=(x^2+y^2)+8x+16`

Use the equations:
`x^2+y^2=r^2, x=rcos theta, y=rsin theta`

`0=r^2+8rcostheta+16`