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

Question

1459 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-10-07T16:52:22

$r^2+8rsintheta=0$

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 $r^2+8rsintheta=0$

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