Hi! This is my first time on Physics Forum. (which shows how desperate I am on figuring out this question). 1. The problem statement, all variables and given/known data r(t) = <3sin(t),4cos(t)> There is a unique circle with the following properties: 1. It passes through the point r(∏/2) 2. At the point r(∏/2), the tangent line to r(t) and the tangent line to the circle are the same. 3. The radius of the circle is 1/κ, where κ is the curvature of r(t) at t = ∏/2 4. The center of the circle lies on the concave side of the surve 2. Relevant equations κ = |dT/ds| T = r'(t)/||r'(t)|| N = T'(t)/||T'(t)|| Not sure if I need more equations for this?? 3. The attempt at a solution So I know that the graph they gave is an elipse, so I can easily visualize what the hint #2 says. I know how to find curvature, so that gives me the radius of the circle. I just need the center. Based on the info above, the center lines on the concave side of the curve. So that means it's in the same direction as N(t). But not sure where to go from there. Any help would be greatly appreciated.