Where would the zero cost point be on the cost function counter plot?

I am learning about the visualization examples of cost functions in contour plots. I wonder where would the zero cost point be on the cost function counterplot. So, would the zero cost points be on the innermost oval in the contour plot, or is it the center point in the plot that is not on any of the oval?

There may not be a zero cost. Perhaps the data is not a perfect fit to any cost function curve.

The goal is to find the minimum cost - not where the cost is zero.

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