$(5$ points$)$ Find the minimum distance between the origin and the surface $in{R}^3$ given $by$:

$z^2=(x-2{)}^2+(y+3{)}^2-xy$

Give both the minimum distance and the coordinates $(x,y,z)of$ the point $(or$ points$)on$ the surface that $is(or$ are$)$ closest $to$ the origin. Hint: $In$ order $to$ start you need $to$ identify a function $f(x,y)$ that you want $to$ optimize.