Explanation Given: 25 x 2 − 36 x y + 40 y 2 − 12 13 x − 8 13 y = 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 25 x 2 − 36 x y + 40 y 2 − 12 13 x − 8 13 y = 0 . A = 25 , B = − 36 and C = 40 ; Cot ( 2 θ ) = A − C B ; 25 − 40 − 36 = − 15 − 36 = 5 12 ; cos 2 θ =

11th Edition

ISBN: 9780135189405

Author: Michael Sullivan

Publisher: PEARSON

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Chapter 10.5, Problem 29AYU

To determine

The appropriate rotation formula to use so that new equation contains no $x y$ term: $25 x^{2} - 36 x y + 40 y^{2} - 12 \sqrt{13} x - 8 \sqrt{13} y = 0$ .

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Chapter 10.5, Problem 28AYU

Chapter 10.5, Problem 30AYU

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The appropriate rotation formula to use so that new equation contains no x y term: 25 x 2 − 36 x y + 40 y 2 − 12 13 x − 8 13 y = 0 .

The appropriate rotation formula to use so that new equation contains no xy term: 25 x 2 − 36xy + 40 y 2 − 12 13 x − 8 13 y = 0 .

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The appropriate rotation formula to use so that new equation contains no $x y$ term: $25 x^{2} - 36 x y + 40 y^{2} - 12 \sqrt{13} x - 8 \sqrt{13} y = 0$ .