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Problems(1)

Geometry of certain points on a hyperbola

Source:

4/19/2013
Consider two points A(x1,y1)A(x_1, y_1) and B(x2,y2)B(x_2, y_2) on the graph of the function y=1xy = \frac{1}{x} such that 0<x1<x20 < x_1 < x_2 and AB=2⋅OAAB = 2 \cdot OA, where O=(0,0)O = (0, 0). Let CC be the midpoint of the segment ABAB. Prove that the angle between the xx-axis and the ray OAOA is equal to three times the angle between the xx-axis and the ray OCOC.
geometryconicshyperbolafunction