Rotate the axes to eliminate the xy-term in the equation: 2x^2 – 3xy – 2y^2 + 5 = 0. Then write the equation in standard form

Answer 1

cot 2θ = (A - C) / b

cot 2θ = (2 + 2) / -3

cot 2θ = 4 / -3

tan 2θ = -3 / 4

tan 2θ = -0.75

2θ = -36.87

θ = -18.43

sin θ = -0.316

cos θ = 0.949

x = 0.949x' + 0.316y'

y = -0.316 - 0.949y'

Substitute for x and y values in original equation, simplify (with a lot of arithmetic!) and convert to standard form (hyperbola).