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Consider the ellipse defined by the equation 2x² + 3xy +2y2 = 1/7 Find a linear change of coordinates (x, y)→ (u, v) that transforms the equation of the ellipse into the standard form 85 + 12 b2 = 1 for some constants a and b. What is the geometric interpretation of the new basis?

Consider the ellipse defined by the equation 2x² + 3xy +2y2 = 1/7 Find a linear change of coordinates (x, y)→ (u, v) that transforms the equation of the ellipse into the standard form 85 + 12 b2 = 1 for some constants a and b. What is the geometric interpretation of the new basis?

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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1. Consider the ellipse defined by the equation 2x² + 3xy + 2y² = 1/7 Find a linear change of coordinates (x, y) → (u, v) that transforms the equation of the ellipse into the standard form u² P v² = 1 for some constants a and b. What is the geometric interpretation of the new basis?
Transcribed Image Text:1. Consider the ellipse defined by the equation 2x² + 3xy + 2y² = 1/7 Find a linear change of coordinates (x, y) → (u, v) that transforms the equation of the ellipse into the standard form u² P v² = 1 for some constants a and b. What is the geometric interpretation of the new basis?
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