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Can someone give me an explanation to hyperbola

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A hyperbola is an open curve with two branches, the intersection of a plane with both halves of a double cone. The plane does not have to be parallel to the axis of the cone; the hyperbola will be symmetrical in any case.

Can someone give me an explanation to hyperbola-example-1
User Alizelzele
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Answer:

its a symmetrical open curve formed by the intersection of a circular cone with a plane at a smaller angle with its axis than the side of the cone.

Explanation: