Rotation of Axes · Exercise 49

Graph the equation relative to the $x^{{}^{\prime }}{y}^{{}^{\prime }}$ system in which the equation has no $x^{{}^{\prime }}{y}^{{}^{\prime }}$ term.

$11x^2+10\sqrt{3}xy+y^2-64=0$

Its source prints no answer for this problem, so there's nothing to check against.

OpenStax, Algebra and Trigonometry 2e · §12.4 Rotation of Axes · Exercise 49