Find the shortest distance from the origin to the surface $z ^ { 2 } = 2 x y + 2$ .
A) $\frac { 1 } { 2 }$
B) $\frac { 1 } { \sqrt { 2 } }$
C)1
D) $\sqrt { 2 }$
E)2
F) $2 \sqrt { 2 }$
G)4
H) $4 \sqrt { 2 }$

Question

Find the shortest distance from the origin to the surface $z ^ { 2 } = 2 x y + 2$ .
A) $\frac { 1 } { 2 }$ 
B) $\frac { 1 } { \sqrt { 2 } }$ 
C)1
D) $\sqrt { 2 }$
E)2
F) $2 \sqrt { 2 }$  
G)4
H) $4 \sqrt { 2 }$

Quizplus · Accepted Answer

The shortest distance from the origin to the surface is found by minimizing the distance function $d = \sqrt{x^2 + y^2 + z^2}$ subject to the constraint $z^2 = 2xy + 2$. Using the method of Lagrange multipliers, the minimum distance is $\sqrt{2}$.

Find the Shortest Distance from the Origin to the Surface z2=2xy+2z ^ { 2 } = 2 x y + 2z2=2xy+2

Find the Shortest Distance from the Origin to the Surface $z ^ { 2 } = 2 x y + 2$