I'm not sure what method you are using here. The curver(t) = (2cos(t),3sin(t)) is an ellipse centred at the origin, with its axes parallel to the coordinate axes. When ,r(t) is the point (0,3) on the y-axis, so the centre of curvature will also be on the y-axis. To locate it, you just need to know the radius of curvature at that point.

With and , the curvature is given by . Evaluate that at , then the radius of curvature is , and that will tell you where the centre of curvature is.