Conical Section

Conic section also called conic in geometry any curve produced by the intersection of a plane and a right circular cone.

Conical section. Conic sections are formed on a plane when that plane slices through the edge of one or both of a pair of right circular cones stacked tip to tip. Definition of a frustum of a right circular cone. Every conic section has certain features including at least one focus and directrix.

The three types are parabolas ellipses and hyperbolas. Whether the result is a circle ellipse parabola or hyperbola depends only upon the angle at which the plane slices through. Representing a line tangent to a hyperbola opens a modal common tangent of circle hyperbola 1 of 5.

Did you know that by taking different slices through a cone you can create a circle an ellipse a parabola or a hyperbola. When a cone is cut by a plane making an angle with the axis greater than the generators of the cone make with the axis and so as to cut both the end generators of the cone the conic section will be an ellipse. In figure a the plane 2 cuts the axis of the cone so as to produce an ellipse as shown in figure c.

Depending on the angle of the plane relative to the cone the intersection is a circle an ellipse a hyperbola or a parabola. The lateral surface of the cone is called a nappe. The conic sections are the nondegenerate curves generated by the intersections of a plane with one or two nappes of a cone.

A section or slice through a cone. In mathematics a conic section or simply conic is a curve obtained as the intersection of the surface of a cone with a plane the three types of conic section are the hyperbola the parabola and the ellipse. The ancient greek mathematicians studied conic sections culminating around 200.

A conic section or simply conic is a curve obtained as the intersection of the surface of a cone with a plane. A conic section a curve that is formed when a plane intersects the surface of a cone. For a plane perpendicular to the axis of the cone a circle is produced.