Explanation Given: x 2 + 4 x y + 4 y 2 + 5 5 y + 5 = 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 x 2 + 4 x y + 4 y 2 + 5 5 y + 5 = 0 . A = 1 , B = 4 and C = 4 ; Cot ( 2 θ ) = A − C B ; 1 − 4 4 = − 3 4

Pearson eText for Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry -- Instant Access (Pearson+)

4th Edition

ISBN: 9780137399635

Author: Michael Sullivan, Michael Sullivan

Publisher: PEARSON+

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Question

Chapter 9.5, Problem 28AYU

To determine

The appropriate rotation formula to use so that new equation contains no $x y$ term: $x^{2} + 4 x y + 4 y^{2} + 5 \sqrt{5} y + 5 = 0$ .

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Chapter 9.5, Problem 27AYU

Chapter 9.5, Problem 29AYU

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Chapter 9 Solutions

Pearson eText for Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry -- Instant Access (Pearson+)

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: x 2 + 4 x y + 4 y 2 + 5 5 y + 5 = 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: $x^{2} + 4 x y + 4 y^{2} + 5 \sqrt{5} y + 5 = 0$ .

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Chapter 9 Solutions

The appropriate rotation formula to use so that new equation contains no x y term: x 2 + 4 x y + 4 y 2 + 5 5 y + 5 = 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: x 2 + 4xy + 4 y 2 + 5 5 y + 5 = 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: $x^{2} + 4 x y + 4 y^{2} + 5 \sqrt{5} y + 5 = 0$ .