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A plane that intersects the vertex of a cone is known as a "vertex plane." This plane can be oriented in various ways, such as being vertical, horizontal, or at an angle, but it must pass through the apex (vertex) of the cone. Depending on the angle of intersection, the resulting shape can vary, producing different conic sections like circles, ellipses, parabolas, or hyperbolas.
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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.
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 what?
circle
If both napped of a right circular cone are intersected by a plane that does not pass through the vertex of the cone what is the resulting curve?
When a plane intersects both nappes of a right circular cone without passing through the vertex, the resulting curve is a hyperbola. This occurs because the plane cuts through both sides of the cone, creating two separate branches of the hyperbola. The precise shape and orientation of the hyperbola depend on the angle at which the plane intersects the cone.
Is it true that given a right circular cone a plane that intersects the cone not at the vertex and is parallel to its edge will always result in a parabola regardless of the shape of the cone?
True.
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 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 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.
If a right circular cone intersects a plane that runs parallel to the edge of the cone the resulting curve is?
The "conic section" that is produced when a right circular cone intersects a plane that runs parallel to the edge of the cone is a parabola. In the case where the plane also intersects the vertex of the cone, the parabola becomes two intersecting lines.
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 the resulting curve will be what?
parabola
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 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 what?
circle
Given a right circular cone a plane that intersects the cone not at the vertex and is parallel to its edge will always result in a parabola regardless of the shape of the cone?
True
If both napped of a right circular cone are intersected by a plane that does not pass through the vertex of the cone what is the resulting curve?
When a plane intersects both nappes of a right circular cone without passing through the vertex, the resulting curve is a hyperbola. This occurs because the plane cuts through both sides of the cone, creating two separate branches of the hyperbola. The precise shape and orientation of the hyperbola depend on the angle at which the plane intersects the cone.
Is it true that given a right circular cone a plane that intersects the cone not at the vertex and is parallel to its edge will always result in a parabola regardless of the shape of the cone?
True.
