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# Identify the quadric surface containing r(t) = <sin(t),cos(t),cos(2t)>. Prove your assertion.?

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- PopeLv 79 months agoFavorite Answer
I see at least two.

z = y² - x² ... hyperbolic paraboloid

x² + y² = 1 ... circular cylinder

Here are two parabolic cylinders, but I am not certain if they fit a strict definition of quadric surface:

z = 1 - 2x²

z = 2y² - 1

- DavidLv 49 months ago
z = cos(2t) = cos²(t) - sin²(t) = y² - x²

z = y² - x²

So the surface is a hyperbolic paraboloid.

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Hm, alright. Stupid me.