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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.
Download as PDF; Printable version; ... Pages in category "Conic sections" ... Parabola; Parabola of safety; Pascal's theorem;
Parabolas have only one focus, so, by convention, confocal parabolas have the same focus and the same axis of symmetry. Consequently, any point not on the axis of symmetry lies on two confocal parabolas which intersect orthogonally (see below). A circle is an ellipse with both foci coinciding at the center.
Download as PDF; Printable version; ... You are free: to share – to copy ... The four conic sections: circle, eclipse, parabola, and hyperbola.
two parabolas, which are contained in two orthogonal planes and the vertex of one parabola is the focus of the other and vice versa. Focal conics play an essential role answering the question: "Which right circular cones contain a given ellipse or hyperbola or parabola (see below)".
A conic is defined as the locus of points for each of which the distance to the focus divided by the distance to the directrix is a fixed positive constant, called the eccentricity e. If 0 < e < 1 the conic is an ellipse, if e = 1 the conic is a parabola, and if e > 1 the conic is a hyperbola.
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.
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.