Why this is a Elliptic Paraboloid?? Let $x^2+2z^2-6x-y+10=0$ and we know that $z/c=x^2/a^2+y^2/b^2$ shows a Elliptic Paraboloid. if we compelete the square we gonna have $(y-1)=(x-3)^2+2z^2.$ Book says we can see that it's a Elliptic Paraboloid which I don't understand it. the equation is not similar at all. Thanks

It'a an elliptic paraboloid pointing in the $y$-direction. The standard formula is pointing in the $z$-direction.