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If a point lies on the conic section, its polar is the tangent through this point to the conic section. If a point P lies on its own polar line, then P is on the conic section. Each line has, with respect to a non-degenerated conic section, exactly one pole.
In mathematics, the matrix representation of conic sections permits the tools of linear algebra to be used in the study of conic sections. It provides easy ways to calculate a conic section's axis , vertices , tangents and the pole and polar relationship between points and lines of the plane determined by the conic.
Download as PDF; Printable version; In other projects ... Tangent half-angle formula; U. ... Media in category "Conic sections"
A conic is the curve obtained as the intersection of a plane, called the cutting plane, with the surface of a double cone (a cone with two nappes).It is usually assumed that the cone is a right circular cone for the purpose of easy description, but this is not required; any double cone with some circular cross-section will suffice.
A conic section is the intersection of a cone with equation + = and a plane. In other words, in space, all conics are defined as the solution set of an equation of a plane and of the equation of a cone just given. This formalism allows one to determine the positions and the properties of the focuses of a conic.
Area#Area formulas – Size of a two-dimensional surface; Perimeter#Formulas – Path that surrounds an area; List of second moments of area; List of surface-area-to-volume ratios – Surface area per unit volume; List of surface area formulas – Measure of a two-dimensional surface; List of trigonometric identities
Brahmagupta's formula; Bretschneider's formula; Compass and straightedge constructions. Squaring the circle; Complex geometry; Conic section. Focus; Circle. List of circle topics; Thales' theorem; Circumcircle; Concyclic; Incircle and excircles of a triangle; Orthocentric system; Monge's theorem; Power center; Nine-point circle; Circle points ...
6 points on the sides of triangle and their common conic section. Carnot's theorem (named after Lazare Carnot) describes a relation between conic sections and triangles.. In a triangle with points , on the side , , on the side and , on the side those six points are located on a common conic section if and only if the following equation holds: