1. ## Geometry/Topology: Hyperbolic Parametrization

Hi!

I'm to find the hyperbolic length of a curve composed of three lines, from P=i, to R = ti, to S = 4 + ti, to Q = 4+i, where t>0, and then find which t makes this value minimal. I've got the formula for hyperbolic length, but it's in terms of x(t) and y(t), and I basically don't know how to actually parametrize the curve so I can fit it in the formula & integrate properly.

( L = $[\int x'(t)^2 + y'(t)^2) / y(t)]$

I get the sense this is seriously basic stuff, but if anyone could help me out I'd really appreciate it. Thanks.

2. PR: x(s)=0, y(s)=s s in [1,t]
RS: x(s)= s, y(s)=t and s in [0,4]
SQ: x(s)=4 y(s)=s s in [t,1]

I changed your t (in the equation for L) with s, cause we have already t as a parameter and not as a dumby variable in the integral.
and the fact that I wrote that s is in ___, is for the integration limits.