Rotate the axes to eliminate the xy-term in the equation: 13x^2 + (6√3)xy + 7y^2 – 48 = 0. Then write the equation in standard form.

Answer 1

cot 2θ = (A - C) / B

cos 2θ = 1 / √3

tan 2θ = √3

θ2 = π/3

θ = π/6

sin π/6 = 1/2

cos π/6 = √3 / 2

x = x' cos π/6 - y' sin π/6

y = x' sin π/6 - y' cos π/6

x = x'√3 / 2 - y' / 2

y = x' / 2 - y'√3 / 2

Now substitute into original equation and simplify into standard form