The plane x y 2z 2 intersects the paraboloid z x 2 y 2 in an ellipse Find the points on this ellipse that are nearest to and farthest from the origin

Question: The plane x + y + 2z = 2 intersects the paraboloid z = x 2 + y 2 in an ellipse. Find the points

The plane x + y + 2z = 2 intersects the paraboloid z = x² + y² in an ellipse. Find the points on this ellipse that are nearest to and farthest from the origin.

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