#An elliptic paraboloid
var('x y z')
gr = implicit_plot3d((z/7) == (x/5)^2 + (y/3)^2, (x,-10,10), (y,-10,10), (z,0,20), axes=True, aspect_ratio=[1,1,1])
show(gr)

#A hyperbolic paraboloid
var('x y z')
gr = implicit_plot3d((z/2) == (x/5)^2 - (y/3)^2, (x,-15,15), (y,-15,15), (z,-15,15), axes=True, aspect_ratio=[1,1,1])
show(gr)

#An ellipsoid
var('x y z')
gr = implicit_plot3d((x/5)^2 + (y/3)^2 + (z/7)^2 == 1, (x,-7,7), (y,-7,7), (z,-8,8), axes=True, aspect_ratio=[1,1,1])
show(gr)