hyperbola
cone +++ A sphere or other full solid of revolution generated about either axis where the curve meets that axis in 2 places, and those intercepts are the solid's poles. (A cone has 2 faces)
The most interesting intersections of cone are its planar sections (intersections with a plane). These sections are called "conic" The figures can be 1) dot - for plane going through apex 2) two lines - for plane containing cone axis 3) one line - for plane going through apex and touching the cone 3) circle - for plane orthogonal to cone axis 4) ellipsis - for plane that intersects the cone axis and generating lines 5) parabola - for plane parallel to a generating line 4) hyperbola - other cases See wikipedia's "conic section" article
circle
It depends on your the inclinantion of the plane which is used to "slice" the cone. The answer can be a circle, ellipse, parabola, hyperbola or two intersecting lines. These (apart from the last) are known as conic sections. In terms of the 2-d figure that generates a cone, the answer is a straight line, with a non-zero slope, rotated about the x-axis.
Circle: If the knife is perpendicular to the axis of the cone.Ellipse: If the knife is between (perpendicular to the axis of the cone) and (parallel to the side of the cone).Parabola: If the knife is between (parallel to the side of the cone) and (parallel to the axis of the cone).Hyperbola: If the knife is parallel to the axis of the cone.Triangle: If the knife is perpendicular to the base of the cone.Point: If the knife is parallel to the base the cone and through the apex
Tilt of cutting plane is between (perpendicular to axis of the cone) and (parallel to the side of 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 is a pair of hyperboles.
Helix
The answer depends on the angle at which the axis of the cone intersects the cross-sections.
It is a section formed by a plane at right angles to the axis of the cone.
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.
On ripening of seeds the cone axis alongates and the seeds get out by wind velocity
a circle
ellipse
The axis of a right circular cone is perpendicular to every radius or diameter of the base.
Circle.