Final answer:
To find the closest points on the cone z² = x² * y² to (6, 2, 0), one must minimize the distance function using calculus, possibly through Lagrange multipliers, considering the constraint imposed by the equation of the cone.
Step-by-step explanation:
The question asks to find the points on the cone z² = x² * y² that are closest to the point (6, 2, 0). To solve this, we must minimize the distance between a point on the cone and the given point. Using calculus, we can set up a function for the distance squared between the point (x, y, z) on the cone and the point (6, 2, 0), which would be D² = (x-6)² + (y-2)² + z². The equation of the cone imposes the constraint z² = x² * y². We then use Lagrange multipliers to solve for the points (x, y, z) that minimize the distance function subject to the constraint imposed by the cone equation.