The plane x + y + 2z = 30 intersects the paraboloid z = x^2 + y^2 in an ellipse. Find the points on the ellipse that are nearest to and farthest from the origin.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section11.2: Ellipses
Problem 46E
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The plane x + y + 2z = 30 intersects the paraboloid z = x^2 + y^2 in an ellipse. Find the points on the ellipse that are nearest to and farthest from the origin.

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