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Hyperbola

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Q: If a plane intersects a right circular cone through both nappes what conic section is created?
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Which conic section is created if a plane intersects a right circular cone through both nappes?

A hyperbola.


If a right circular cone intersects a plane that goes through both nappes of the cone but not through the vertex the resulting curve will be what?

if a right circular cone intersects a plane that goes through both nappes of the cone, but not through the vertex, the resulting curve will be a hyperbola


If a right circular intersects a plane that runs perpendicular to the cones axis but does not pass through its vertex the resulting curve will be an?

If a right circular cone intersects a plane that runs perpendicular to the cone's axis but does not pass through its vertex the resulting curve will be a circle.


If a right circular cone intersects a plane that runs parallel to the cone's axis but does not pass through its vertex?

If a right circular cone intersects a plane that runs parallel to the cone's axis but does not pass through its vertex, the resulting curve is a pair of hyperboles.


If a right circular cone intersects a plane that runs perpendicular to the cone's axis but does not pass through its vertex the resulting curve will be a n?

If a right circular cone intersects a plane that runs perpendicular to the cone's axis but does not pass through its vertex the resulting curve will be a circle.


What is it called when a plane intersects a right circular cone through both nappes?

The intersection forms a hyperbola.


If a Right circular cone intersects a plane that runs parallel to the cone's axis but does not pass through its vertex the resulting curve will be what?

parabola


If a right circular cone intersects a plane that runs perpendicular to the cones axis but does not pass through its vertex the resulting curve will be an?

circle


If a right circular cone intersects a plane that runs parallel to the cone's axis but does not pass through its vertex the resulting curve will be an?

hyperbola


If a right circular cone intersects a plane that runs perpendicular to the cone's axis but does not pass through its vertex the resulting curve will be an?

circle


If a right circular cone intersects a plane that runs parallel to the cones axis but does not pass through its vertex the resulting curve will be a?

parabola


What if a right circular cone intersects a plane that passes through one of its nappes but the plane is not parallel to an edge of the cone?

Then the intersection is a hyperbola.