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## Homework Statement

Consider the points P = (1/2, √3/2) and Q = (1,1). They lie on the half circle of radius one centered at (1,0).

a) Use the deifnition and properites of the hyperbolic distance (and length) to compute d

_{H}(P,Q).

b) Compute the coordinates of the images of Pa nd Q through the standard inversion and use that to evaluate again d

_{H}(P,Q).

## Homework Equations

Our professor gave us a few trig identites to use, but other than that we need the equation for Hyperbolic distance:

∫ [itex]\sqrt{}x'(t)

^{2}+y'(t)

^{2}[/itex] [itex]\frac{}{}y(t)[/itex]

From a to b where a < t < b

## The Attempt at a Solution

Ignoring the question almost entirely, the part that I can't figure out is how to parameterize this correctly. My professor gave us a solution that gave one option for a parameterization, but I'm not sure how he got there.

His solution:

x(t) = cost +1

y(t)= sint

I believe that more than one parameterization would work, but how do you come up with the one that makes things simplest?

Thank you so much!

Phoenix