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In geometry, focuses or foci (/ ˈ f oʊ k aɪ /; sg.: focus) are special points with reference to which any of a variety of curves is constructed. For example, one or two foci can be used in defining conic sections, the four types of which are the circle, ellipse, parabola, and hyperbola.
These are the three vertices A such that d(A, B) ≤ 3 for all vertices B. Each black vertex is a distance of at least 4 from some other vertex. The center (or Jordan center [1]) of a graph is the set of all vertices of minimum eccentricity, [2] that is, the set of all vertices u where the greatest distance d(u,v) to other vertices v is
When the outer Soddy circle has negative curvature, its center is the isoperimetric point of the triangle: the three triangles formed by this center and two vertices of the starting triangle all have the same perimeter. [4] Triangles whose outer Soddy circle degenerates to a straight line with curvature zero have been called "Soddyian triangles ...
The linear eccentricity of an ellipse or hyperbola, denoted c (or sometimes f or e), is the distance between its center and either of its two foci. The eccentricity can be defined as the ratio of the linear eccentricity to the semimajor axis a : that is, e = c a {\displaystyle e={\frac {c}{a}}} (lacking a center, the linear eccentricity for ...
The midpoint of the line segment joining the foci is called the center of the hyperbola. [6] The line through the foci is called the major axis . It contains the vertices V 1 , V 2 {\displaystyle V_{1},V_{2}} , which have distance a {\displaystyle a} to the center.
This yields the center as given below. An alternative approach that uses the matrix form of the quadratic equation is based on the fact that when the center is the origin of the coordinate system, there are no linear terms in the equation. Any translation to a coordinate origin (x 0, y 0), using x* = x – x 0, y* = y − y 0 gives rise to
The "vertex centroid" comes from considering the polygon as being empty but having equal masses at its vertices. The "side centroid" comes from considering the sides to have constant mass per unit length. The usual centre, called just the centroid (centre of area) comes from considering the surface of the polygon as having constant density ...
In a hyperbola the following are concurrent: (1) a circle passing through the hyperbola's foci and centered at the hyperbola's center; (2) either of the lines that are tangent to the hyperbola at the vertices; and (3) either of the asymptotes of the hyperbola.