Hi I new here and I hope to get som help with a problem i cant seem to figur out.

I need to find the ellipsoid of the form ax^2 + by^2 + cz^2 = 1 that fits best to a bunch of points:

p1: x=2 y=2 z=-1

p2: x=1 y=2 z=0

p3: x=-3 y=1 z=2

p4: x=-1 y=2 z=2

p5: x=3 y=-3 z=2

p6: x=2 y=0 z=2

p7: x=1 y=-2 z=2

p8: x=1 y=-1 z=1

p9: x=-3 y=2 z=2

I really hope you can help me solve this problem!