Yes, it is true that if 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. There are four cases... Plane perpendicular to axis: circle
Plane between perpendicular to axis and parallel to edge: ellipse
Plane parallel to edge: parabola
Plane between parallel to edge and parallel to axis: hyperbolehttp://en.wikipedia.org/wiki/Conic_section
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.
A Parabola.
parabola
That's true. The qualifying phrase "no matter the shape" is meaningless ... the shape has already been completely specified by the earlier part of the question.
yes because they will always equal 180 degrees, regardless of the angle at which the transversal intersects the two parallel lines
True
True.
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.
A Parabola.
Parabola
A parabola.
parabola
parabola
The intersection of the cone and that particular plane is a parabola.
If a right circular cone intersects a plane that runs parallel to the edge of the cone the result curve will be a parabola, unless the intersection includes the vertex of the cone, in which case the intersection is a straight line. This is a conic section. Depending on the angle of the plane, the section will be a circle, an ellipse, a parabola, or two hyperboles.
The intersection of a right circular cone and a plane that is parallel to the edge of the cone is a parabola. However, if the vertex of the cone lies on the plane, then the intersection is simply two intersecting lines.
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.