MathDB

CIIM 2011 Problem 6

Source:

June 9, 2016

CIIMCIIM 2011undergraduate

Problem Statement

Let

\Gamma

be the branch

x> 0

of the hyperbola

x^2 - y^2 = 1.

Let

P_0, P_1,..., P_n

different points of

\Gamma

with

P_0 = (1, 0)

and

P_1 = (13/12, 5/12)

. Let

t_i

be the tangent line to

\Gamma

at

P_i

. Suppose that for all

i \geq 0

the area of the region bounded by

t_i, t_{i +1}

and

\Gamma

is a constant independent of

i

. Find the coordinates of the points

P_i

.

Back to Problems View on AoPS