Answer
$${x^2} + {y^2} = 4$$
Work Step by Step
$$\eqalign{
& r = 2 \cr
& {\text{Square both sides}} \cr
& {r^2} = 4 \cr
& {\text{Use }}{r^2} = {x^2} + {y^2} \cr
& {x^2} + {y^2} = 4 \cr} $$
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.