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The plane x + y + 2z = 10 intersects the paraboloid z = x² + y² in an ellipse. Find the points on this ellipse that are nearest to and farthest from the origin. Point farthest away occurs at ( Point nearest occurs at

The plane x + y + 2z = 10 intersects the paraboloid z = x² + y² in an ellipse. Find the points on this ellipse that are nearest to and farthest from the origin. Point farthest away occurs at ( Point nearest occurs at

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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#### Geometry and Calculus Problem: Intersection of a Plane and a Paraboloid The plane \( x + y + 2z = 10 \) 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. - Point farthest away occurs at \( ( \ \underline{\hspace{50px}} \ , \ \underline{\hspace{50px}} \ , \ \underline{\hspace{50px}} \ ) \). - Point nearest occurs at \( ( \ \underline{\hspace{50px}} \ , \ \underline{\hspace{50px}} \ , \ \underline{\hspace{50px}} \ ) \).
Transcribed Image Text:#### Geometry and Calculus Problem: Intersection of a Plane and a Paraboloid The plane \( x + y + 2z = 10 \) 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. - Point farthest away occurs at \( ( \ \underline{\hspace{50px}} \ , \ \underline{\hspace{50px}} \ , \ \underline{\hspace{50px}} \ ) \). - Point nearest occurs at \( ( \ \underline{\hspace{50px}} \ , \ \underline{\hspace{50px}} \ , \ \underline{\hspace{50px}} \ ) \).
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