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All the conic sections share a reflection property that can be stated as: All mirrors in the shape of a non-degenerate conic section reflect light coming from or going toward one focus toward or away from the other focus. In the case of the parabola, the second focus needs to be thought of as infinitely far away, so that the light rays going ...
A pencil of confocal ellipses and hyperbolas is specified by choice of linear eccentricity c (the x-coordinate of one focus) and can be parametrized by the semi-major axis a (the x-coordinate of the intersection of a specific conic in the pencil and the x-axis). When 0 < a < c the conic is a hyperbola; when c < a the conic is an ellipse.
The name "parabola" is due to Apollonius, who discovered many properties of conic sections. It means "application", referring to "application of areas" concept, that has a connection with this curve, as Apollonius had proved. [1] The focus–directrix property of the parabola and other conic sections was mentioned in the works of Pappus.
Media in category "Conic sections" This category contains only the following file. Drawing an ellipse via two tacks a loop and a pen 2.jpg 480 × 640; 24 KB
The hyperbola is one of the three kinds of conic section, formed by the intersection of a plane and a double cone. (The other conic sections are the parabola and the ellipse. A circle is a special case of an ellipse.) If the plane intersects both halves of the double cone but does not pass through the apex of the cones, then the conic is a ...
As a space curve, a spherical conic is a quartic, though its orthogonal projections in three principal axes are planar conics. Like planar conics, spherical conics also satisfy a "reflection property": the great-circle arcs from the two foci to any point on the conic have the tangent and normal to the conic at that point as their angle bisectors.
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.
Consisting of 32 propositions, the work explores properties of and theorems related to the solids generated by revolution of conic sections about their axes, including paraboloids, hyperboloids, and spheroids. [1] The principal result of the work is comparing the volume of any segment cut off by a plane with the volume of a cone with equal base ...