The plane r+y+z= 12 intersects the paraboloid z = r2 + y2 in an ellipse. Find...

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The plane r+y+z= 12 intersects the paraboloid z = r2 + y2 in an ellipse. Find the points on the ellipse that are nearest to a

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Answer 1

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given plane Xtyzz= 12 Paraboloidz ał tyto 9 = x+y+za12 f= xty-z=0 Extreme value of the sanare a the distance to the origeon D Is 1822=0 .2=1, then xty = 7 has no solution 30, 2 - 24 itan try all+24) YOlten) suzy t = nty- zzo & 9=atyt} 212 . .22-2=0 2x

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The plane r+y+z= 12 intersects the paraboloid z = r2 + y2 in an ellipse. Find...