I don't fully understand the process of finding the center of curvature. I've been looking through my book and the only thing it shows explicitly is that the radius of curvature is 1/k. What is the general method to find the center of the circle?

For example: Find an equation of the circle of curvature of the curve .

I can find quickly that the radius is 1/2, but I don't see how to find the center. I'm looking for something general that I could apply to more difficult problems. Any help is appreciated.