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If a plane intersects a right circular cone through both nappes what conic section is created?
Hyperbola
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 are all the the cross sections of a sphere?
The cross sections of a sphere can be circular or elliptical, depending on how the plane intersects the sphere. When a plane cuts through the center of the sphere, the cross section is a circle with the same radius as the sphere. If the plane intersects the sphere at an angle or does not pass through the center, the cross section will still be a circle, but its radius will be smaller than that of the sphere. Additionally, if the plane is tangent to the sphere, the cross section reduces to a single point.
What is it called when a plane intersects a right circular cone through both nappes?
The intersection forms a hyperbola.
If a plane intersects a right circular cone through both nappes what conic section is created?
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 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 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 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 are all the the cross sections of a sphere?
The cross sections of a sphere can be circular or elliptical, depending on how the plane intersects the sphere. When a plane cuts through the center of the sphere, the cross section is a circle with the same radius as the sphere. If the plane intersects the sphere at an angle or does not pass through the center, the cross section will still be a circle, but its radius will be smaller than that of the sphere. Additionally, if the plane is tangent to the sphere, the cross section reduces to a single point.
What is it called when a plane intersects a right circular cone through both nappes?
The intersection forms a hyperbola.
What is the intersection of a plane passing through the apex of a right circular cone?
The intersection of a plane passing through the apex of a right circular cone is a conic section. Depending on the angle at which the plane intersects the cone, it can result in different shapes: if the plane is parallel to the base of the cone, it produces a circle; if it cuts through the cone at an angle, it can yield an ellipse, parabola, or hyperbola. The specific type of conic section formed is determined by the orientation and position of the plane relative to the cone.
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
