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The distance from (3,-6,4) to a point (x,y,z) on the paraboloid is
d^2 = (x-3)^2 + (y+6)^2 + (z-4)^2
= (x-3)^2 + (y+6)^2 + (x^2+y^2-4)^2
the partials of z are zero at (1,-2) and d^2 = 21
For centroids, just plug in to the formula. Should not be hard.