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The Kiepert hyperbola is a hyperbola and triangle conic that is related to the solution of Lemoine's problem and its generalization to isosceles triangles constructed on the ...

A curve and its polar reciprocal with regard to the fixed conic have the same Halphen transformation.

A triangle that is equal to its polar triangle with respect to a given conic is said to be self-polar with respect to that conic. Any triangle is self-polar with respect to ...

A hyperbola (plural "hyperbolas"; Gray 1997, p. 45) is a conic section defined as the locus of all points P in the plane the difference of whose distances r_1=F_1P and ...

Let lambda be the longitude, lambda_0 the reference longitude, phi the latitude, phi_0 the reference latitude, and phi_1 and phi_2 the standard parallels. Then the ...

A circumhyperbola is a circumconic that is a hyperbola. A rectangular circumhyperbola always passes through the orthocenter H and has center on the nine-point circle ...

The conic sections are the nondegenerate curves generated by the intersections of a plane with one or two nappes of a cone. For a plane perpendicular to the axis of the cone, ...

A skew conic, also known as a gauche conic, space conic, twisted conic, or cubical conic section, is a third-order space curve having up to three points in common with a ...

Given a point P, the point P^' which is the antipodal point of P is said to be the antipode of P. The term antipode is also used in plane geometry. Given a central conic (or ...

The directrix of a conic section is the line which, together with the point known as the focus, serves to define a conic section as the locus of points whose distance from ...