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The difference, major or not, is that an eclipse and a hyperbola are not related, at all.

You might have meant to say "Ellipse". In that case, an ellipse is a closed line shape of which the left and right bouts are symmetrical and the top and bottom bouts are also symmetrical. A hyperbola can never close, and only its left and right parts are symmetrical.

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Q: What is the major difference between an eclipse and a hyperbola?
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