Below are the Maple commands that generate the various standard quadric surfaces.
In the Maple worksheet you can click and drag within an image in order to view the quadric surface from various angles.
> plot3d([6*sin(s)*cos(t),4*sin(s)*sin(t),3*cos(s)],s=0..Pi, t=0..2*Pi,
axes=none, scaling=constrained, orientation=[-45,60],
title=`Ellipsoid \n a=6, b=4, c=3`);
> plot3d([6*cosh(s)*cos(t),4*cosh(s)*sin(t),3*sinh(s)],s=-1..1, t=-Pi..Pi,
axes=none, scaling=constrained, orientation=[-45,60],
title=`Hyperboloid of 1 sheet\n a=6, b=4, c=3`);
> plot3d({[6*cosh(s),4*sinh(s)*cos(t),3*sinh(s)*sin(t)],
[-6*cosh(s),4*sinh(s)*cos(t),3*sinh(s)*sin(t)]},s=-2..2, t=-Pi..Pi,
axes=none, scaling=constrained, orientation=[-45,60],
title=`Hyperboloid of 2 sheets\n a=6, b=4, c=3`);
> plot3d([6*s*cos(t),4*s*sin(t),3*s^2],s=0..3, t=0..2*Pi,axes=none,
scaling=constrained, orientation=[-45,60],
title=`Elliptic Paraboloid \n a=6, b=4, c=3`);
> plot3d({[6*s*cosh(t),4*s*sinh(t),3*s^2],[6*s*sinh(t),4*s*cosh(t),-3*s^2]},
s=-4..4, t=-2..2,axes=none, scaling=constrained, orientation=[-65,70],
title=`Hyperbolic Paraboloid \n a=6, b=4, c=3`);
