Match each equation with the quadric surface it describes. $($Each option should be used only once.$)$

$$ ellipsoid

$x^2+y^2+z^2=1$

sphere

cone

hyperbolic paraboloid

$x^2+2y^2+3z^2=1$

elliptic paraboloid

$x^2-y^2=z$

hyperboloid of one sheet

$x^2-y^2+z^2=1$

hyperboloid of two sheets

$x^2-y^2-z^2=1$