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.
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.
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter7: Conic Sections And Quadratic Systems
Section7.CT: Chapter Test
Problem 11CT
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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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