How can I form the parameterization of a curve of intersection given a sphere $x^2+y^2+z^2 =1$ and an elliptic cylinder $2x^2 + z^2 = 1$ ?
2026-03-26 12:57:55.1774529875
Parametrizing the curve of intersection between a elliptic cylinder and a sphere
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Thanks to @WillJagy$${x={\cos t\over \sqrt 2}\\y={\cos t\over \sqrt 2}\quad ,\quad t\in \Bbb R\\z=\sin t}$$and $${x={\cos t\over \sqrt 2}\\y=-{\cos t\over \sqrt 2}\quad ,\quad t\in \Bbb R\\z=\sin t}$$ Comment
My original answer suggested just one of those branches while there are two. The images below suggest why: