Plz helppp: Identify the graph of the equation. What is the angle of rotation for the equation? 21x^2-8√3 xy+13y^2=225
2 answers:
Answer:
The correct option is C.
C) ellipse, -30°
Step-by-step explanation:
General form of equation for a conic section is:
(A)x² + (B)xy + (C)y² + (D)x + (E)y + F = 0
The equation of the conic section is given:
21x² - (8√3)xy + 13y² = 225
21x² - (8√3)xy + 13y² - 225 = 0
Which can be rewritten as:
(21)x² + (-8√3)xy + (13)y² + (0)x + (0)y + (-225) = 0
where
A = 21
B = -8√3
C = 13
D = 0
E = 0
F = -225
Consult the table below.
As A ≠ C and and AC > 0 , the equation represents an ellipse
The angle of rotation can be found by following equation:
cot(2θ) = (A - C)/B
cot(2θ) = (21 - 13)/(-8√3)
2θ = cot⁻¹(8/-8√3)
2θ = 120°
θ = 60° (from x-axis)
As the major axis of ellipse lies on y-axis, axis of rotation from y-axis is
θ = -30°
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