MathDB

Geometry of certain points on a hyperbola

Source:

April 19, 2013

geometryconicshyperbolafunction

Problem Statement

Consider two points

A(x_1, y_1)

and

B(x_2, y_2)

on the graph of the function

y = \frac{1}{x}

such that

0 < x_1 < x_2

and

AB = 2 \cdot OA

, where

O = (0, 0)

. Let

C

be the midpoint of the segment

AB

. Prove that the angle between the

x

-axis and the ray

OA

is equal to three times the angle between the

x

-axis and the ray

OC

.

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