Make the change of variables
$x = u \cos \theta - v \sin \theta$
$y = u \sin\theta + v \cos \theta$
where the angle $0\le \theta < \pi/2$ is chosen in order to eliminate the cross product term in
$x^2 + xy + y^2 = 6$
Then find the standard form of equation in the $( u, v )$ variables. (Enter a function of $( u,v)$.)
$= 1 .$