Answer
$$r=\pm2$$
Work Step by Step
Since
$$ x=r\cos \theta,\quad y=r\cos \theta, \quad z=z,$$
then $ x^2+y^2=4$ takes the form
$$ r^2\cos^2\theta+r^2\sin^2\theta =4 \\
r^2=\frac{4}{\cos^2\theta+\sin^2\theta}=4 \\
r=\pm2$$
You can help us out by revising, improving and updating this answer.
Update this answerAfter you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.