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

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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.
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
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.

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looks more like a parabolic elliptic cone thingamjig to me
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otherwise its not a surface, and is meant to be a curve:
well in 3d it is as surface. I get a cylinder on grapher. Not any close to answering the question though :(.

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