Answer
Option C is correct.
Angle of rotation = θ = 45.0°
Explanation
For a given conic section with general formula
Ax² + Bxy + Cy² + Dx + Ey + F = 0
The angle of rotation is given as
Angle of rotation = θ
Cot (2θ) = A - CB
For our question, the general formula is
x² + xy + y² = 10
x² + xy + y² - 10 = 0
where
A = 1
B = 1
C = 1
D = 0
E = 0
F = -10
To find angle of rotation,
Cot (2θ) = A - CB
Cot (2θ) = 1 - (1) (1)
Cot (2θ) = 1 - 1
Cot (2θ) = 0
2θ = Cot⁻¹ (0)
2θ = 90°
Divide both sides by 2
(2θ/2) = (90°/2)
θ = 45.0°
Hope this Helps!!!
