I have this question about linear geometry. For the equation $$2x^2+3y^2+az^2-2xy+4z-5=0$$ I have to find for which values of $a$ do I get:
- a parabolic cylinder,
- a pair of parallel planes.
I've a lead: for $a>0$, $a<0$ and $a=0$, bring each case to its canonical form and then I am stuck.
Thanks for the help. Benny.