Explanation Given: 13 x ² − 6 √ 3 x y + 7 y ² − 16 = 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, 13 x ² − 6 √ 3 x y + 7 y ² − 16 = 0 . A = 13 , B = − 6 3 and C = 7 ; Cot ( 2 θ ) = A − C B ; 13 − 7 − 6 3 = �...

Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (4th Edition)

4th Edition

ISBN: 9780134686974

Author: Michael Sullivan, Michael Sullivan III

Publisher: PEARSON

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Question

Chapter 9.5, Problem 25AYU

To determine

The appropriate rotation formula to use so that new equation contains no $x y$ term: $13 x ² - 6 \sqrt 3 x y + 7 y ² - 16 = 0$ .

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Chapter 9.5, Problem 24AYU

Chapter 9.5, Problem 26AYU

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Chapter 9 Solutions

Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (4th Edition)

Ch. 9.2 - The formula for the distance d from P 1 =( x 1 , y...Ch. 9.2 - To complete the square of x 2 4x , add_______...Ch. 9.2 - Use the Square Root Method to find the real...Ch. 9.2 - The point that is symmetric with respect to the...Ch. 9.2 - To graph , shift the graph of to the...Ch. 9.2 - A(n)_______ is the collection of all point in a...Ch. 9.2 - True or false The line through the focus and...Ch. 9.2 - For the parabola , the line segment joining the...Ch. 9.2 - Answer Problems 9-12 using the figure. If , the...Ch. 9.2 - Answer Problems 9-12 using the figure. The...

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The appropriate rotation formula to use so that new equation contains no x y term: 13 x ² − 6 √ 3 x y + 7 y ² − 16 = 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: $13 x ² - 6 \sqrt 3 x y + 7 y ² - 16 = 0$ .

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Chapter 9 Solutions

The appropriate rotation formula to use so that new equation contains no x y term: 13 x ² − 6 √ 3 x y + 7 y ² − 16 = 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: 13x² − 6√3xy + 7y² − 16 = 0 .

Want to see the full answer?

Chapter 9 Solutions

The appropriate rotation formula to use so that new equation contains no $x y$ term: $13 x ² - 6 \sqrt 3 x y + 7 y ² - 16 = 0$ .