Multivariate Calculus: multivariate calculus – #22701

Question: The plane \(z-x-y=8\) intersects the cone \({{z}^{2}}={{x}^{2}}+{{y}^{2}}\) form a curve in 3 dimensions, so there are points that are on the intersection of both of those surfaces. Find the point lying on the intersection of both the cone and the plane that is closest to the origin. Write this as a constrained optimization problem (i.e., g(x,y,z) = c1, etc). Then give (but don’t solve!) the list of all equations that would be used to find this point.

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