Find Shortest Distance from z2+3x-xy=9 to Origin

[theown1]

Homework Statement

a) what is the shortest distance from the surface z²+3x-xy=9 to the origin?

Homework Equations

I know that when you take the gradient of an equation the gradient is perp. to the vector and gives the direction of largest rate of inc.

The Attempt at a Solution

so I took the gradient of f(x,y,z) and i got
f_x=3-y
f_y=-x
f_z=2z
I tried looking at these and thinking of it as a parameterized line and i got an answer of (3,0,0) but I don't think that it is right..
now I'm still a little confused on what i should do next, can someone help point me in the right direction?

 

[Sethric]

The gradient won't help you find distance to the origin. I would recommend Lagrange multipliers here.