Find the radius of the largest sphere centered at the origin that could be inscribed by the ellipsoid:
2(x+1)^2 + y^2 + 2(z-1)^2 = 8

Question

Find the radius of the largest sphere centered at the origin that could be inscribed by the ellipsoid:
2(x+1)^2 + y^2 + 2(z-1)^2 = 8

anonymous · Answer

my guess on how to approach this problem would be to use the distance formula and differentiate to find the minimum distance from the origin to the surface, which would in turn be the radius of the maximum inscribed sphere... but I'm not sure how to incorporate the equation of the ellipsoid into the distance formula...

anonymous · Answer

alternately, perhaps you could just find the critical points of the ellipsoid and plug them into the distance formula to test and see which is the smallest? But I feel like that's a less reliable solution since the ellipsoid isn't centered around the origin..

anonymous · Answer

Maybe change to polar cords.  Then you have $\rho$ which could be minimized.

anonymous · Answer

http://tutorial.math.lamar.edu/Classes/CalcIII/LagrangeMultipliers.aspx minimize x^2+y^2+z^2 given the constraint

anonymous · Answer

righteo. forgot about those... Thanks!