Final answer:
The required angle of rotation to remove the xy term from the equation is π/6, which corresponds to the answer choice B. This is calculated using the formula for rotation of axes in conic sections. Therefore, θ = π/6. the correct option is B. π/6
Step-by-step explanation:
The question asks for the angle of rotation required to remove the xy term from the equation 9x² + 2√3xy + 7y² = 10. Rotating the axes that diagonalize the quadratic form associated with the equation can eliminate the xy term.
The formula to determine the angle θ is given by θ = 1/2 √ an⁻¹(2b/(a-c)), where a is the coefficient of x², b is the coefficient of xy, and c is the coefficient of y². In this case, a = 9, b = √3, and c = 7. Plugging these values into the formula gives us θ = 1/2 √ an⁻¹(2√3/(9-7)) = 1/2 √ an⁻¹(√3) = π/6. Thus, the correct answer is B. π/6.
To remove the xy term in the equation 9x²+2√3xy+7y²=10, we need to find the angle of rotation of the axes. The angle of rotation can be found using the formula:
tan(2θ) = (2√3) / (9-7) = √3 / 1 = √3
Therefore, θ = π/6. the correct option is B. π/6