1. The problem statement, all variables and given/known data Find a formula for the curvature of the curve: x=(e^t + e^(-t))/2 y=(e^t - e^(-t))/2 Write an equation of the osculating circle when t=0. 2. Relevant equations curvature=|x'y'' - x''y'|/(x'^2 + y'^2)^(3/2) 3. The attempt at a solution First, wouldn't the formula for curvature be: sqrt(2) --------- (e^(2t) + e^(-2t))/2 * sqrt(e^(2t) + e^(-2t)) ? But for some reason, my teacher marked a big "X" across this and wrote question marks. EDIT: Nevermind about the first part of the question - I just should have simplified it more. Now, for the equation of the osculating circle when t=0, I'd get the center of the circle by doing: <x_center,y_center>=<x(0)-K*y'(0)/sqrt(x'(0)^2+y'(0)^2),y(0)+K*x'(0)/sqrt(x'(0)^2+y'(0)^2)> where K=curvature?