Rotation of axes to eliminate xy-term & give new equation in xy coordinates

153x^2+192xy+97y^2=225
?? = 0

please help me, this is the only problem I don't understand at all. I know it's ellipse since the discriminant is less than 0.

The general form is Ax² + Bxy + Cy² + Dx + EY + F = 0.

153x² + 192xy + 97y² = 225
153x² + 192xy + 97y² - 225 = 0

A = 153
B = 192
C = 97
D = 0
E = 0
F = -225

cot(2θ) = (A - C)/B
cot(2θ) = (153 - 97)/192 = 7/24

cos(2θ) = 7/25
sinθ = √{[1 - cos(2θ)]/2} = 3/5
cosθ = √(1 - sin²θ) = 4/5

Use these formulas for the coefficients of the rotated curve:

A' = Acos²θ + Bsinθcosθ + Csin²θ
B' = B(cos²θ - sin²θ) - 2(A - C)sinθcosθ
C' = Asin²θ - Bsinθcosθ + Ccos²θ
D' = Dcosθ + Esinθ
E' = -Dsinθ + Ecosθ
F' = F

A' = 153(16/25) + 192(12/25) + 97(9/25) = 225
B' = 192[(16/25) - (9/25)] - 2(153 - 97)(12/25) = 0
C' = 153(9/25) - 192(12/25) + 97(16/25) = 25
D' = 0
E' = 0
F' = -225

Rotated equation:
225x² + 25y² - 225 = 0
9x² + y² - 9 = 0