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

66 A particle moves along a circular path over a horizontal xy coordinate system, at constant speed. At time $t_1 = 5.00 \text{ s}$, 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?