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…

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…