http://www.wolframalpha.com/input/?i=31x%5E2%2B10sqrt(3)xy%2B(108*sqrt(3)%2B32)x%2B(108*sqrt(3)-32)y%2B244%3D0 :Wolfram

31x^2+10\sqrt{3}xy+(108*\sqrt{3}+32)x+(108*\sqrt{3}-32)y+244=0 :desmos