Can you help me understand what a parabolic cylinder is in the context of this problem?

Can you help me understand what a parabolic cylinder is in the context of this problem?
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answer:I’m just guessing here, but it sounds to me that instead of a normal cylinder with a circular wall, the cylinder you’re looking at here is ovoid (if closed), meaning that sections of it would have a parabolic curved wall. Here are some examples, if it helps.
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