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  3. the plane x + y + 2z = 12 intersects the paraboloi

The plane x + y + 2z = 12 intersects the paraboloid z = x2 + y2 in an...

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Question

Basic Math

The plane

x + y + 2z = 12

intersects the paraboloid

z = x2 + y2

in an ellipse. Find the points on the ellipse that are nearestto and farthest from the origin.

nearest point    (x, y, z)=
  
farthest point    (x, y, z)=
  

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