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

Multiple Choice

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) $4 \sqrt { 2 }$