Find the equation of the common part of two objects

Question

How to find the equation of the intersection curve of the ball $ x^2 + y^2 + z^2 = 4a^2 $ (1)and the cylinder $x^2+y^2=2ax(a>0)$(2)?

let (1)-(2), we can get $$z^2+2ax-4a^2=0 $$ but this is not the curve equation because $y$ is missing.

Answer 1

It is the Viviani's curve https://en.wikipedia.org/wiki/Viviani's_curve