Identify the conic with th e given equa­tion and give its equation in standard form 6x^2 - 4xy + 9y^2 - 20x - 10y - 5 = 0

Given $6x^2-4xy+9y^2-20x-10y-5=0$ All degenerate conic sections have equations of the form $A{x}^2+Bxy+C{y}^2+Dx+Ey+F=0$.
$A{x}^2+Bxy+C{y}^2+Dx+Ey+F=0$ where A,B,C,D,E and F are constants. If $B^2-4AC$ is less than zero, if a conic exists and A = C, it will be a circle If $B^2-4AC$ is less than zero, if a conic exists , it will be ellipse. If $B^2-4AC$ equals zero, if a conic exists, it will be a parabola. If $B^2-4AC$ is greater than zero, if a conic exists, it will be a hyperbola. Here in equation $6x^2-4xy+9y^2-20x-10y-5=0$, $B^2-4AC=4^2-4\cdot 6\cdot 9$
$=16-216$
$=-200<0$ and $A\ne C$ Hence it is an ellipse