Final answer:
To eliminate the xy term, use a rotation of axes by finding the angle and substituting x and y with new variables.
Step-by-step explanation:
To eliminate the xy term in the equation 11x² - 24xy + 4y² + 20 = 0, we can use a rotation of axes. The rotation should be such that the new x and y axes are aligned with the major and minor axes of the ellipse represented by the equation. The angle of rotation can be found using the formula:
θ = 0.5 * atan( (2 * B) / (A - C) )
where A = 11, B = -12, and C = 4. Once we determine the angle of rotation, we can substitute x and y with new variables u and v, where:
u = x*cos(θ) - y*sin(θ)
v = x*sin(θ) + y*cos(θ)
By substituting these variables, the xy term can be eliminated and we can solve the simplified equation.