Explanation Calculation: Consider the given information as, x y + 3 = 0 Rotate the axes to eliminate the x y - term in the equation x y + 3 = 0 . The general second-degree equation where B ≠ 0 is: A x 2 + B x y + C y 2 + D x + E y + F = 0 If B ≠ 0 , then the above equation can be written as, A ′ x ′ 2 + C ′ y ′ 2 + D ′ x ′ + E ′ y ′ + F ′ = 0 Where, cot 2 θ = A − C B Compare the provided equation with the second-degree equation as, A = 0 , B = 1 and C = 0 Rotate the coordinate axes through an angle θ . Now, to evaluate the value of θ , use the formula cot 2 θ = A − C B and substitute the values of A , B and C in it. cos 2 θ = A − C B = 0 − 0 1 = 0 For cot 2 θ = 0 , the value of θ is evaluated as: 2 θ = π 2 θ = π 4 Then, obtain the equation in the x ′ y ′ − system by substitution as, x = x ′ cos θ − y ′ sin θ y = x ′ sin θ + y ′ cos θ Substitute the value in the above equation as, x = x ′ cos θ − y ′ sin θ x = x ′ cos π 4 − y ′ sin π 4 x = x ′ 1 2 − y ′ 1 2 x = x ′ − y ′ 2 And, y = x ′ sin θ + y ′ cos θ y = x ′ sin π 4 + y ′ cos π 4 y = x ′ 1 2 + y 1 2 y =

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ISBN: 9781337278461

Author: Ron Larson

Publisher: Cengage Learning

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Chapter 6.5, Problem 13E

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To calculate: The given equation xy+3=0 in standard form after rotating the axis to remove the xy-term. Also, sketch its graph.

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Chapter 6.5, Problem 12E

Chapter 6.5, Problem 14E

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The given equation x y + 3 = 0 in standard form after rotating the axis to remove the x y -term . Also, sketch its graph.

Solution Summary: The author calculates the given equation xy+3=0 in standard form after rotating the axes to remove the

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To calculate: The given equation xy+3=0 in standard form after rotating the axis to remove the xy-term. Also, sketch its graph.

Want to see the full answer?

Chapter 6 Solutions