If I have equation
3x^2+3y^2-2xy-8x+8y-z+10=0
How can I get determinant
A=[ 3 -1 0]
[ -1 3 0]
[0 0 0]

***This is about isometric transformation.I know what is the fundamental equation-(Ax^2+2Bxy+Cy^2+Dx+Ey+F=0) but how can I set up this A determinant?

Question

If I have equation 
3x^2+3y^2-2xy-8x+8y-z+10=0
How can I get determinant
A=[  3      -1      0]
     [ -1       3      0]
     [0         0      0]

***This is about isometric transformation.I know what is the fundamental equation-(Ax^2+2Bxy+Cy^2+Dx+Ey+F=0) but how can I set up this A determinant?

p0sitr0n · Answer

I'm confused, do you want the discriminant for the equation or the determinant of the matrix?

canimcan · Answer

Discriminant for the equation

canimcan · Answer

Conic Sections General Form: A x2 + B xy + C y2 + D x + E y + F = 0

canimcan · Answer

I hope you understand ,🙈
It can be some other equation but I don't know rule to get this A dicriminant or matrix ..
For example this equation
5x^2+5y^2-4z^2-2xy-4xz-4yz=0
Have matrix 
A=[5     -1     -2 ]
     [-1     5      -2]
     [-2     -2     -4]
How?
If you don't realize what I don't understand I 'll explain better👀

p0sitr0n · Answer

From what I got you want |A| or det(A). In your original question, i can right away say that the determinant is 0. You can see it via cofactor expansion along the last row or last column.

canimcan · Answer

In equation in my original questions i have A=3 ,B=-1,
so i put that in the first row of A.
it will be A=[3    -1   0]
next row of A is[ -1 3 0] ?! I don't understand that.