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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.

canoe
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1 Answers1

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

Jean Marie
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  • It cannot be of the form $z=f(x,y)$, because it would be the equation of a surface ; but here it a (space) curve (intersection of two surfaces). – Jean Marie Feb 29 '16 at 13:27