Discriminants for ellipse, parabola or hyperbola

[duki]

Homework Statement

Use the discriminant to determine if the following are equations of an ellipse, parabola or hyperbola

$$6x^2-12xy+6y^2-5x+9=0$$
$$5xy-4y^2+8x-3y+20=0$$
$$x^2-9xy+5y^2-2=0$$
$$10x^2-9xy+5y^2-2=0$$
$$2y^2-10x+9y-8=0$$

Homework Equations

The Attempt at a Solution

I got these answers:

$$0, parabola$$
$$25, hyperbola$$
$$44, hyperbola$$
$$-119, ellipse$$
$$0, parabola$$

could someone check me on these? Thanks!

 

[Dick]

Shouldn't the third one be 81-4*1*5=61,hyperbola? Was that so hard you really needed a check?