Joke zzox

The tangent plane of the surface is xXo-2yYo+2zZo= 1.

Find the shortest distance, the tangent plane is parallel to the plane x+y+z=2.

That is XO/1=-2yo/1= 2zo/1.

That is Xo=-2Yo=2Zo.

That is 2 zzo+2yZo+2 zzo = 1.

That is 2Zo(x+y+z)= 1.

∴Zo≠0

∴x+y+z= 1/2Zo

The distance of ∴ is |2- 1/2Zo|

Let Zo=a

Then the point (2a, -a, a) is the tangent point and satisfies the curve equation.

(2a)？ -2(-a)？ +2(a)？ = 1

The solution is a = 1/2.

∴ When a=- 1/2, that is, the point (-1, 1/2,-1/2) has the longest distance to the plane, and the longest distance is 3.

When a= 1/2, that is, the point (1,-1/2, 1/2) has the shortest distance to the plane, and the shortest distance is 1.