It will be a hyperbola.
hyperbola
An Ellipse
ellipse
Two nappes of a right circular cone meet at a point called the vertex.
It is the vertex. It can also be called the apex but that has a connotation of being the top-most point and so is not appropriate when both nappes are concerned.
hyperbola
hyperbola
An Ellipse
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 a hyperbola
A line is produced
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, the resulting curve will bea(n) _____ . ellipse
CIRCLE!
ellipse
If I understand your question correctly, it would be an ellipse.
Two nappes of a right circular cone meet at a point called the vertex.
Hyperbola