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
$208 x^2 + 288 xy + 292 y^2 + 1120 x + 1160 y = 38300$
Then find the standard form of equation in the $( u, v )$ variables. (Enter a function of $(u,v)$. )
$= 1.$