Question

Which intersection forms a hyperbola?
A plane intersects both nappes of a double-napped cone, and the plane does not intersect the vertex.
A plane intersects only one nappe of a double-napped cone, and the plane is parallel to the generating line of the cone.
A plane intersects only one nappe of a double-napped cone, and the plane is perpendicular to the axis of the cone.
A plane intersects only one nappe of a double-napped cone, and the plane is not parallel to the generating line of the cone.

Answer 1

"A plane intersects both nappes of a double-napped cone, and the plane does not intersect the vertex" forms a hyperbola.

Answer: Option A

Step-by-step explanation:

Hyperbola can define in different ways as follows:  

• Intersection of a straight round double cone with the surface at an angle greater than the slope of the cone (e.g., perpendicular to the cone’s base).
• The set of all points is the difference between the distances to the fixed two focal points
• A set of all point, to which ratio to the distance to focus divided by the distance to the line (directrix) is greater than one .

Answer 2

Answer:

A plane intersects both nappes of a double-napped cone, and the plane does not intersect the vertex.

Step-by-step explanation:

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