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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.
From the fact, that the affine image of a conic section is a conic section of the same type (ellipse, parabola,...), one gets: Any plane section of an elliptic cone is a conic section. Obviously, any right circular cone contains circles. This is also true, but less obvious, in the general case (see circular section).
The concept of geometrical continuity was primarily applied to the conic sections (and related shapes) by mathematicians such as Leibniz, Kepler, and Poncelet.The concept was an early attempt at describing, through geometry rather than algebra, the concept of continuity as expressed through a parametric function.
More generally, when the directrix is an ellipse, or any conic section, and the apex is an arbitrary point not on the plane of , one obtains an elliptic cone [4] (also called a conical quadric or quadratic cone), [5] which is a special case of a quadric surface.
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
In mathematics, a generalized conic is a geometrical object defined by a property which is a generalization of some defining property of the classical conic.For example, in elementary geometry, an ellipse can be defined as the locus of a point which moves in a plane such that the sum of its distances from two fixed points – the foci – in the plane is a constant.
In Euclidean geometry, a circumconic is a conic section that passes through the three vertices of a triangle, [1] and an inconic is a conic section inscribed in the sides, possibly extended, of a triangle. [2] Suppose A, B, C are distinct non-collinear points, and let ABC denote the triangle whose vertices are A, B, C.
Congruent conic sections Two conic sections are congruent if their eccentricities and one other distinct parameter characterizing them are equal. Their eccentricities establish their shapes, equality of which is sufficient to establish similarity, and the second parameter then establishes size.