Something like this?
M = 10; (*Number of points*)
data = RandomReal[1, {M, 2}]; (*Generate coords of points*)
Show[RegionPlot[BoundingRegion[data, "MinDisk"]], Graphics[{Red, Point /@ data}]] (*Calculate Circumdisk and plot*)
In 3D
data3d = RandomReal[1, {M, 3}];
Show[RegionPlot3D[BoundingRegion[data3d, "MinBall"], PlotStyle -> Directive[Yellow, Opacity[0.5]]], Graphics3D[{Red, Point /@ data3d}]]
Cheers,
Marco
