Graphs of equations in 4D cartesian coordinates

[darthbadass]

In 3D, the graph of

x^2/a^2 +/- y^2/b^2 +/- z^2/c^2=0

where a, b and c are positive constants and not all three algebraic signs are negative is called a central quadric surface. Logically, in 4D, the equation should look something like this:

x^2/a^2 +/- y^2/b^2 +/- z^2/c^2 +/- w^2/d^2=0

I believe it would be called a central quadric hypersurface (ie a 3D volume stretched into the 4th degree of freedom). Can anyone confirm this?

[jinydu]

Yes that sounds reasonable. And we know that the "surface" generated by the equation will be 3D because we have 4 dimensions and 1 constraint, hence 3 degrees of freedom.