Answer to Question #6391 in Calculus for Russell

Question

Find the equation for the circle of curvature of the curve r(t)=(sqrt2)(t)(ihat) + (t^2)(jhat) at the point (sqrt8, 4) (this curve parameterizes the curve y=(1/2)(x^2) in the xy-plane)

Along with the problem please explain
1. What value of t corresponds to the indicated coordinates?
2. What elements will you need for the equation of the circle?
3. What values and vectors will aide you in finding the elements of the circle?
4. How will you use these values and vectors to obtain the necessary elements?