Explanation Given: 34 x 2 − 24 x y + 41 y 2 − 25 = 0 Formula used: To transform A x 2 + B x y + C y 2 + D x + E y + F = 0 , B ≠ 0 into an equation in x ′ and y ′ without an x ′ y ′ -term, rotate the axes through an angle θ that satisfies the equation Cot ( 2 θ ) = A − C B . x = x ′ cos θ − y ′ sin θ ; y = x ′ sin θ + y ′ cos θ Calculation: Consider the given equation 34 x 2 − 24 x y + 41 y 2 − 25 = 0 . A = 34 , B = − 24 and C = 41 ; Cot ( 2 θ ) = A − C B ; 34 − 41 − 24 = − 7 − 24 = ...

11th Edition

ISBN: 9780135189405

Author: Michael Sullivan

Publisher: PEARSON

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Chapter 10.5, Problem 30AYU

To determine

The appropriate rotation formula to use so that new equation contains no $x y$ term: $34 x^{2} - 24 x y + 41 y^{2} - 25 = 0$ .

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Chapter 10.5, Problem 29AYU

Chapter 10.5, Problem 31AYU

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The appropriate rotation formula to use so that new equation contains no x y term: 34 x 2 − 24 x y + 41 y 2 − 25 = 0 .

Solution Summary: The author determines the appropriate rotation formula to use so that new equation contains no x y term.

The appropriate rotation formula to use so that new equation contains no $x y$ term: $34 x^{2} - 24 x y + 41 y^{2} - 25 = 0$ .

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Chapter 10 Solutions

Additional Math Textbook Solutions

The appropriate rotation formula to use so that new equation contains no x y term: 34 x 2 − 24 x y + 41 y 2 − 25 = 0 .

Solution Summary: The author determines the appropriate rotation formula to use so that new equation contains no x y term.

The appropriate rotation formula to use so that new equation contains no xy term: 34 x 2 − 24xy + 41 y 2 − 25 = 0 .

Want to see the full answer?

Chapter 10 Solutions

Additional Math Textbook Solutions

The appropriate rotation formula to use so that new equation contains no $x y$ term: $34 x^{2} - 24 x y + 41 y^{2} - 25 = 0$ .