Question

Can anyone help me about this problem..thank you already
Find the points on the ellipsoid
(x^2)/(5^2)+(y^2)/(2^2)+(z^2)/(10^2)=1
that are closest and farthest away from the point (2,0,4).

Answer 1

since the point is on the y = 0 can we just consider the cross section cutting the y = 0 ?

Answer 2

i just want to say i'll try and help, i havent done anything like this before in school

Answer 3

yes i know it's different than others

Answer 4

ok i think we can use parametric equations to do it. i worked out the parametric eq for the ellipsoid by stretching the unit sphere.

sphere:

\[x = \cos \phi \cos \theta \text{ , } y = \cos \phi \sin \theta \text{ , } z = \sin \phi\]

so for the ellipsoid we get


\[x = acos \phi \cos \theta \text{ , } y = bcos \phi \sin \theta \text{ , } z = csin \phi\]

which satisfies the Cartesian equation nicely

now i'll try to find the distances