Mediaspace scheduled maintenance: Aug 25, 2026 07:00 - 12:00 AM. During this time, videos will be temporarily unavailable. Check status updates.

Lecture

Conic Sections: Basics and Properties

Description

This lecture covers the fundamental concepts related to conic sections, including the properties of the circle, ellipse, hyperbola, and parabola. The instructor explains the equations, degenerate cases, and geometric interpretations of these curves, focusing on the cross product, mixed product, and right properties. Emphasis is placed on understanding the center, asymptotes, and special characteristics of each conic section.

This video is available exclusively on Mediaspace for a restricted audience. Please log in to MediaSpace to access it if you have the necessary permissions.

Watch on Mediaspace

Official source

Ontological neighbourhood

Mathematics

Geometry: Euclidean geometry

Related concepts (32)

Hyperbola

In mathematics, a hyperbola (haɪˈpɜrbələ; pl. hyperbolas or hyperbolae -liː; adj. hyperbolic ˌhaɪpərˈbɒlɪk) is a type of smooth curve lying in a plane, defined by its geometric properties or by equations for which it is the solution set. A hyperbola has two pieces, called connected components or branches, that are mirror images of each other and resemble two infinite bows. The hyperbola is one of the three kinds of conic section, formed by the intersection of a plane and a double cone.

Unit hyperbola

In geometry, the unit hyperbola is the set of points (x,y) in the Cartesian plane that satisfy the implicit equation In the study of indefinite orthogonal groups, the unit hyperbola forms the basis for an alternative radial length Whereas the unit circle surrounds its center, the unit hyperbola requires the conjugate hyperbola to complement it in the plane. This pair of hyperbolas share the asymptotes y = x and y = −x.

Ellipse

In mathematics, an ellipse is a plane curve surrounding two focal points, such that for all points on the curve, the sum of the two distances to the focal points is a constant. It generalizes a circle, which is the special type of ellipse in which the two focal points are the same. The elongation of an ellipse is measured by its eccentricity , a number ranging from (the limiting case of a circle) to (the limiting case of infinite elongation, no longer an ellipse but a parabola).

Circle

A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre. The distance between any point of the circle and the centre is called the radius. Usually, the radius is required to be a positive number. A circle with (a single point) is a degenerate case. This article is about circles in Euclidean geometry, and, in particular, the Euclidean plane, except where otherwise noted. Specifically, a circle is a simple closed curve that divides the plane into two regions: an interior and an exterior.

Parabola

In mathematics, a parabola is a plane curve which is mirror-symmetrical and is approximately U-shaped. It fits several superficially different mathematical descriptions, which can all be proved to define exactly the same curves. One description of a parabola involves a point (the focus) and a line (the directrix). The focus does not lie on the directrix. The parabola is the locus of points in that plane that are equidistant from the directrix and the focus.

Related lectures (31)

Conic Sections: Determining Parameters

Explores the determination of conic section parameters and the laws of Kepler in celestial mechanics.

Sphere, Cone, and Cylinder: Descriptive Geometry

Explores spheres, cones, and cylinders, including intersections, ruled surfaces, and conic sections with practical examples.

Analytical Geometry: Conic Sections Log in to Mediaspace to watch this video

Covers the properties and equations of conic sections.

Conic Sections: Ellipse and Hyperbola Log in to Mediaspace to watch this video

Explores properties of conic sections, center, equations, and coordinate transformations.

Conics in the Plane: Uniform Description of 3 Conics Log in to Mediaspace to watch this video