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 A. ellipse, 75 degrees
B. hyperbola, -60 degrees
C. ellipse, -30 degrees
D. hyperbola, 90 degrees

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°