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7.2.1 Show that a quadratic form ax² + bxy + cy² may be converted to a form a'x¹2 + b'y2 by suitable choice of 0 in the substitution x = x' cos 0 - y sin 0, y = x' sin 0 + y' cos 0, by checking that the coefficient of x'y is (c − a) sin 20+ b cos 20. 7.2.2 Deduce from Exercise 7.2.1 that, by suitable rotation of axes, any quadratic curve may be expressed in the form a'x² + b'y² + c²x + d'y + e' = 0.

7.2.1 Show that a quadratic form ax² + bxy + cy² may be converted to a form a'x¹2 + b'y2 by suitable choice of 0 in the substitution x = x' cos 0 - y sin 0, y = x' sin 0 + y' cos 0, by checking that the coefficient of x'y is (c − a) sin 20+ b cos 20. 7.2.2 Deduce from Exercise 7.2.1 that, by suitable rotation of axes, any quadratic curve may be expressed in the form a'x² + b'y² + c²x + d'y + e' = 0.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Hi I need the answer for 7.2.2

7.2.1 Show that a quadratic form ax² + bxy + cy² may be converted to a form a'x¹² + b'y'² by suitable choice of in the substitution x = x' cos 0 - y sin 0, y = x' sin 0 + y' cos 0, by checking that the coefficient of x'y' is (c- a) sin 20+ bcos 20. 7.2.2 Deduce from Exercise 7.2.1 that, by suitable rotation of axes, any quadratic curve may be expressed in the form a'x² +b'y² + c²x + ď'y' + e' = 0.
Transcribed Image Text:7.2.1 Show that a quadratic form ax² + bxy + cy² may be converted to a form a'x¹² + b'y'² by suitable choice of in the substitution x = x' cos 0 - y sin 0, y = x' sin 0 + y' cos 0, by checking that the coefficient of x'y' is (c- a) sin 20+ bcos 20. 7.2.2 Deduce from Exercise 7.2.1 that, by suitable rotation of axes, any quadratic curve may be expressed in the form a'x² +b'y² + c²x + ď'y' + e' = 0.
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