Define the symmetric C of O w.r. to B(x

1) The tangent at B defines a segment DE between the asymptotic lines which is bisected by B.

2) The area of all [asymptotic] triangles ODE (depend on B) is constant and equal to 2x

3) Since every hyperbola can be obtained from the standard one (defined through y=1/x) through an affinity, the two previous results are valid for all hyperbolas (see HyperbolaFromRectangular.html ).

The rectangular hyperbola is among the hyperbolas the analogon of the circle among ellipses. There are though significant differences. For example, three points in general position define a unique circle containing them, whereas rectangular hyperbolas are uniquely determined by four points in general position (and non-orthocentric).

Hyperbola.html

HyperbolaAsymptoticProperty.html

HyperbolaAsymptotics.html

HyperbolaFromRectangular.html

OrthoRectangular.html

RectangularAsProp.html

RectHyperbola.html

RectHyperbolasTangent4Lines.html

RectHypeImpossible.html

RectHypeRelation.html

RectHyperbolaTriaInscribed.html

RectHypeThroughFourPts.html

Produced with EucliDraw© |