Conjugate diameters perpendicular to each other are called, axes, and the points where they cut the…

The cone is sliced by a hyperbola within a plane. The angle of the hyperbola will make a smaller angle…

Diagram of a cone with spheres and cut by a plane to depict the conic sections.

Diagram of a cone with inscribed spheres and cut by various planes to depict the conic sections: circle,…

Diagram showing how to construct a conic when given the focus and the auxiliary circle. If the focus…

Diagram showing how to construct a conic when given the focus and the auxiliary circle. The focus is…

Diagram showing how to construct a conic when given the focus and the auxiliary circle. As the focus…

Illustration showing a hyperbola as a curve formed by the intersection of the surface of a cone with…

Illustration showing the asymptotes of a hyperbola. The asymptotes will never meet the curve.

Illustration of a hyperbola and its auxiliary circle. "Any ordinate of a hyperbola is to the tangent…

Diagram depicting a cone with both nappes intersected by plane J to form a hyperbola.

Illustration of a cone cut by a plane parallel to the axis of the cone and perpendicular to the vertical…

Illustration showing the definition of a hyperbola as a conic section.

Illustration showing the definition of an hyperbola as a conic section. A hyperbola is formed from a…

An illustration showing the intersection of a plane and a double cone. The cone is intersected by a…

Illustration showing how the a hyperbola is symmetrical with respect to its conjugate axis.

Any two conjugate diameters of an hyperbola are harmonic conjugates with regard to the asymptotes.

Illustration showing how a hyperbola con be constructed by points, having been given the foci and the…

An illustration showing how to construct a hyperbola by plotting. "Having given the transverse axis…

An illustration showing how to construct a hyperbola by a pencil and a string. "Having given the transverse…

Illustration showing the definition of an hyperbola. "An hyperbola may be described by the continuous…

Illustration of a hyperbola with distances to foci drawn. "The difference of the distances of any point…

Illustration of a hyperbola with a line bisecting the focal radii. "If through a point P of an hyperbola…

Illustration of a point on a hyperbola. "If d denotes the abscissa (x-coordinate) of a point of an hyperbola,…

Illustration showing how to draw a tangent to an hyperbola from a given point P on the convex side of…

Diagram part of a hyperbola with a tangent line that illustrates "A line through a point on the hyperbola…

All triangles formed by a tangent and the asymptotes of an hyperbola are equal in area.

Three dimensional representation of a variable hyperbola moving parallel to itself along the parabolas…

Two dimensional representation of variable hyperbola moving parallel to itself along the parabolas as…

A Lemniscate is, in general, a curve generated by a point moving so that the product of its distances…

The segments between the point of intersection of two tangents to a conic and their points of contact…

Illustration showing intersecting straight lines meeting to form a triangle. It is formed by the intersection…