Classify Quadratic Surfaces: Ellipsoids, Hyperboloids, Paraboloids & Cylinders

[FilipVz]

On the basis of the eigenvalues of A, classify the quadratic surfaces
X'AX+BX+k=0
into ellipsoids, hyperboloids, paraboloids and cylindres.

Can somebody help me to solve the problem?

 

[I like Serena]

On the basis of the eigenvalues of A, classify the quadratic surfaces
X'AX+BX+k=0
into ellipsoids, hyperboloids, paraboloids and cylindres.

Can somebody help me to solve the problem?

Hi FilipVz, welcome to MHB! :)

That is a pretty generic question.
The best I can do is to refer you to the relevant wiki article about Quadrics.