The figure speaks from itself. The central symmetry of the hyperbola and its asymptotics about its center O implies the equality of the red segments AE = BC = ... etc. and the equality of the blue segments DE = FC = ... etc. In other words, every line defines through the hyperbola and its asymptotics two segments having a common middle (f.e. EC, AB). This has an important consequence for recangular hyperbolas (see RectangularAsProp.html ).
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Hyperbola Asymptotic Property ![[0_0]](HyperbolaAsymptoticProperty_files/HyperbolaAsymptoticProperty_0_0_0.png)
![[0_1]](HyperbolaAsymptoticProperty_files/HyperbolaAsymptoticProperty_0_0_1.png)
![[0_2]](HyperbolaAsymptoticProperty_files/HyperbolaAsymptoticProperty_0_0_2.png)
![[1_0]](HyperbolaAsymptoticProperty_files/HyperbolaAsymptoticProperty_0_1_0.png)
![[1_1]](HyperbolaAsymptoticProperty_files/HyperbolaAsymptoticProperty_0_1_1.png)
![[1_2]](HyperbolaAsymptoticProperty_files/HyperbolaAsymptoticProperty_0_1_2.png)