Halliday, Resnick & Walker — Motion in Two and Three Dimensions: Problem 66

A particle moves along a circular path over a horizontal \(xy\) coordinate system, at constant speed. At time \(t_1 = 4.00 \text{ s}\), it is at point \((5.00 \text{ m}, 6.00 \text{ m})\) with velocity \((3.00 \text{ m/s})\hat{j}\) and acceleration in the positive \(x\) direction. At time \(t_2 = 10.0 \text{ s}\), it has velocity \((-3.00 \text{ m/s})\hat{i}\) and acceleration in the positive \(y\) direction. What are the (a) \(x\) and (b) \(y\) coordinates of the center of the circular path if \(t_2 - t_1\) is less than one period?