I know this --- $13x^2 +10xy+13y^2 -42x + 6y -27 =0$ is an ellipse as $h^2=25 < ab=169$ and the discriminant is non-zero.
Am I right ? What more can I say about this curve? Can I get the equation of the ellipse in the usual form if it is an ellipse?
Can anyone please help me ?