shortest point between a distance and a surface?

find the shortest distance between $x^2-xy+y^2=3$ and (0,0)

Question

shortest point between a distance and a surface?

find the shortest distance between $x^2-xy+y^2=3$ and (0,0)

amistre64 · Answer

a surface tends to be 3 dimensional; therefore the given point would have to have 3 components as well in order to reside in the same metric space.

amistre64 · Answer

ideally tho, you would find an equation to the normal plane of the surface that contains the given point and measure your distances within that plane of reference

richyw · Answer

well in this case I am assuming that it means to the point x=0,y=0 where z is arbitrary because it is a cylinder.

amistre64 · Answer

looks more like a parabolic elliptic cone thingamjig to me

amistre64 · Answer

otherwise its not a surface, and is meant to be a curve: http://www.wolframalpha.com/input/?i=x%5E2%E2%88%92xy%2By%5E2%3D3

richyw · Answer

well in 3d it is as surface. I get a cylinder on grapher. Not any close to answering the question though :(.