I tried to set x=t and y= sqrrt(1+t^2) ...it comes out nasty and ugly, so ugly that i didn't even finish it..i'm not sure if there's a better way to do it.
Consider the hyperbola y^2-x^2=1 (y>0)
a.) Find a parameterization for the curve and write it in vector form, R(t)
(b) Calculate the unit tangent vector as a function of the parameter.
(c) Calculate the unit normal vector and the curvature vector as a function of the parameter.