Conic Section Grapher

A conic section is a special class of curves.

Conic section grapher. Every conic section has certain features including at least one focus and directrix. A conic section or simply conic is a curve obtained as the intersection of the surface of a cone with a plane. When a plane intersects a two napped cone conic sections are formed.

A conic section section is a curve generated by intersecting a right circular cone with a plane. An ellipse is generated when the plane is tilted so it intersects each generator but only intersects one nappe. E is the eccentricity of the conic section.

A circle has an eccentricity of zero so the eccentricity shows us how un circular the curve is. The ancient greek mathematicians studied conic sections culminating around 200. The graphic below shows how intersections of a two napped cone and a plane form a parabola ellipse circle and a hyperbola.

The three types are parabolas ellipses and hyperbolas. Conic sections calculator calculate area circumferences diameters and radius for circles and ellipses parabolas and hyperbolas step by step. The circle is a special case of the ellipse though historically it was sometimes called a fourth type.

Usually these constants are referred to as a b h v f and d. Explore the different conic sections and their graphs. In the following interactive you can vary parameters to produce the conics we learned about in this chapter.

Imagine these cones are of infinite height but shown with a particular height here for practical reasons so we can see the extended conic sections. A circle is generated when the plane is perpendicular to the axis of the cone. The curves can also be defined using a straight line and a point called the directrix and focus.