unit hyperbola requires the conjugate hyperbola y 2 − x 2 = 1 {\displaystyle y^{2}-x^{2}=1} to complement it in the plane. This pair of hyperbolas share...

In geometry, a conjugate hyperbola to a given hyperbola shares the same asymptotes but lies in the opposite two sectors of the plane compared to the original...

In mathematics, a hyperbola is a type of smooth curve lying in a plane, defined by its geometric properties or by equations for which it is the solution...

diameters of a hyperbola are conjugate when each bisects all chords parallel to the other. In this case both the hyperbola and its conjugate are sources...

through (a, 0) and (−a, 0). The case a = 1 is called the unit hyperbola. The conjugate hyperbola is given by { z : ‖ z ‖ 2 = − a 2 } {\displaystyle \left\{z:\lVert...

ellipse, parabola, or hyperbola according as the line intersects the circumcircle in 0, 1, or 2 points. The isogonal conjugate of the circumcircle is...

a hyperbola is perpendicular to the conjugate axis and to each directrix. The product of the perpendicular distances from a point P on a hyperbola or...

hyperbola with asymptote A, its reflection in A produces the conjugate hyperbola. Any diameter of the original hyperbola is reflected to a conjugate diameter...

surface intersecting a plane. The three types of conic section are the hyperbola, the parabola, and the ellipse; the circle is a special case of the ellipse...

over 200. Osgood and Graustein used the rectangular hyperbola, its conjugate hyperbola, and conjugate diameters to rationalize tie rods at 15 degree radial...

\over e^{2}-1}.} The transverse axis of a hyperbola coincides with the major axis. In a hyperbola, a conjugate axis or minor axis of length 2 b {\displaystyle...

Lorentz transformation". This diagram included the unit hyperbola, its conjugate, and a pair of conjugate diameters. Since the 1960s a version of this more...

unit hyperbola x2 − y2 = 1, and its conjugate x2 − y2 = −1 can be used to form a polar decomposition based on the branch of the unit hyperbola through...

equation represents a hyperbola; if we also have A + C = 0 {\displaystyle A+C=0} , the equation represents a rectangular hyperbola. A quadric, or quadric...

notions preceded physical interpretation. For instance, conjugate diameters of conjugate hyperbolas are related as space and time. The principle of relativity...

{\displaystyle OI} is tangent to this hyperbola at I {\displaystyle I} . The hyperbola is the isogonal conjugate of O I {\displaystyle OI} , the line joining...

duration lies on a hyperbola. Since the hyperbola is traced by a hyperbolic angle, and velocity determines a point on the hyperbola, there is a hyperbolic...

point (in fact, two complex conjugate lines), or the null set (twice the line at infinity or two parallel complex conjugate lines). All these degenerate...

{\displaystyle \eta } -coordinates such that the wanted conic section appears as a hyperbola and the points U , V {\displaystyle U,V} become the points at infinity...

sections, the four types of which are the circle, ellipse, parabola, and hyperbola. In addition, two foci are used to define the Cassini oval and the Cartesian...

terminology stems from the use of conjugate hyperbolas in the pseudo-Euclidean plane: conjugate diameters of these hyperbolas are hyperbolic-orthogonal. Complemented...

Alvis–Curtis duality Artin–Verdier duality Beta-dual space Coherent duality Conjugate hyperbola De Groot dual Dual abelian variety Dual basis in a field extension...

Edinburgh, and included a sheet of nine figures, two of which display conjugate hyperbolas. Having been stung in the Great Vector Debate over the non-associativity...

Triangle Centers, the outer Vecten point is denoted by X(485). Isogonal conjugate of outer Vecten point is Kenmotu point [ja]. Let △ABC be any given plane...

runs from S1 to P behind the upper part of the hyperbola (see diagram) and is free to slide on the hyperbola. The part of the string from P to F2 runs and...

triangle circle (respectively, ellipse, hyperbola, parabola) is used to denote a circle (respectively, ellipse, hyperbola, parabola) associated with the reference...

relativistic wave equations relativistic mass split-complex number unit hyperbola world line black holes no-hair theorem Hawking radiation Hawking temperature...

point of rotational symmetries. Similarly the centre of an ellipse or a hyperbola is where the axes intersect. Several special points of a triangle are...

{\displaystyle \det A_{33}=AC-{\frac {B^{2}}{4}}} : Q {\displaystyle Q} is a hyperbola if and only if det A 33 < 0 {\displaystyle \det A_{33}<0} , Q {\displaystyle...

{CH}}{\overline {CF}}}=2.} The isogonal conjugate of the orthocenter is the circumcenter of the triangle. The isotomic conjugate of the orthocenter is the symmedian...