min Manhattan distance

[onako]

Given a set of points in 2D, I'm supposed to find a point that
a) minimizes the sum of Manhattan distances to these points
b) minimizes the sum of squared Manhattan distances to these points

For a) I would need to choose a median on x-axis and combine it with the median in y-axis.
But, I'm not sure how b) is different? Any suggestion on how to approach the problem is welcome.
Thanks

[jj7947]

Would you have to compute the walking distance between each point on the x-axis and y-axis?