The hyperbola is uniquely determined by one of its points (M) and the location of its focal points D and E. This is done as follows:

- Draw the bisector BD of the angle at B.

- Construct the circle, whose points on the arc CDA view the segment AC under the angle = ang(EBA).

- The intersection-points D, E of this circle with the bisector BD are the focal points of the hyperbola.

From the construction of D, follows that triangles EBA, CDA and CBE are similar. Angles ang(CAD) = ang(EAB), thus EC' = CD and analogously EA' = AD and B is the middle of ED. The construction here is the inverse of the one discussed in the file AsymptoticTriangle.html .

Hyperbola.html

HyperbolaAsymptotics.html

HyperbolaAsymptoticProperty.html

HyperbolaWRAsymptotics.html

Philon.html

RectangularAsProp.html

RectHyperbola.html

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