The document contains code for plotting various implicit and parametric 3D surfaces in Maple. It includes implicit plots of spheres, ellipsoids, hyperboloids, cylinders, cones and other quadric surfaces defined by implicit equations. It also contains parametric plots describing surfaces like helices, cylinders, tori and surfaces of revolution generated by rotating curves around axes. All plots are generated over the domain -5 to 5 for variables x, y and z with varying numbers of sample points.

1. > with(plots);
SUPERFICIES
> implicitplot3d(x^2+y^2+z^2 = 4, x = -5 ..5, y = -5 .. 5, z = -5 ..5, numpoints=2000, labels=[y,x,
z],axes= NORMAL);
> implicitplot3d(4*x^2+5*y^2-7*z^2 = 4, x = -5 .. 5, y = -5 .. 5, z = -5 .. 5, numpoints=10000, labels
= [y,x,z],axes= NORMAL);
> implicitplot3d(4*x^2-5*y^2-7*z^2 = 4, x = -5 .. 5, y = -5 .. 5, z = -5 .. 5, numpoints= 5000, labels=
[y,x,z], axes= NORMAL);
> implicitplot3d(3*y^2+5*z^2 = 4, x = -5 ..5, y = -5 ..5, z = -5 ..5, numpoints=3000, labels=[y,x,
z],axes= NORMAL);
>
> implicitplot3d(3*y^2-4*z^2= 4, x = -5 .. 5, y = -5 ..5, z = -5 .. 5, numpoints=3000, labels=[y, x,
z],axes= NORMAL);
> implicitplot3d(2*z^2= 16, x = -5 ..5, y = -5 ..5, z = -5 ..5, numpoints=100, labels= [y,x,z], axes
= NORMAL);
> implicitplot3d(4*x^2+3*y^2+2*z^2 = 0, x = -5 ..5, y = -5 ..5, z = -5 .. 5, numpoints=3000, labels
= [y,x,z],axes= NORMAL);
> implicitplot3d(5*x^2+4*y^2-3*z^2 = 0, x = -5 .. 5, y = -5 .. 5, z = -5 .. 5, numpoints=3000, labels=
[y,x,z], axes= NORMAL);

2. > implicitplot3d(-2*y^2-2*z^2 = 0, x = -4 .. 5, y = -5 .. 5, z = -5 .. 5, numpoints=1, labels= [y,x,z],
axes= NORMAL);
> implicitplot3d(-3*y^2+4*z^2 = 0, x = -5 .. 5, y = -5 .. 5, z = -5 .. 5, numpoints= 3000, labels= [y,x,
z],axes= NORMAL);
> implicitplot3d(z^2=0, x = -5 .. 5, y = -5 .. 5, z = -10 .. 10, numpoints=300, labels= [y,x,z],axes=
NORMAL);
> implicitplot3d(z=x^2+y^2, x = -5 .. 5, y = -5 .. 5, z = -5 .. 5, numpoints = 5000, labels= [y,x,z],
axes= NORMAL);
> implicitplot3d(z=x^2-y^2, x = -5 .. 5, y = -5 .. 5, z = -5 .. 5, numpoints= 3500, labels= [y,x,z],
axes= NORMAL);
> implicitplot3d(x^2= z, x = -5 .. 5, y = -5 .. 5, z = -5 .. 5, numpoints=3000, labels=[y,x,z], axes=
NORMAL);
> implicitplot3d(6*x^2+3*y^2 = 0, x = -5 .. 5, y = -5 .. 5, z = -5 .. 5, numpoints= 3000, labels= [y,x,
z],axes= NORMAL);
> implicitplot3d(x^2-y^2= 0, x = -5 .. 5, y = -5 .. 5, z = -5 .. 5, numpoints=300, labels=[y,x, z],axes
= NORMAL);
> implicitplot3d((x^2+(9/4)*y^2+z^2-1)^3-x^2*z^3-(9/80)*y^2*z^3 = 0, x = -1.5 .. 1.5, y = -1.5 ..
1.5, z = -1.5 ..1.5, numpoints=90000, labels= [y,x,z], axes= NORMAL);

3. > implicitplot3d(x^2-z-3=0, x = -5 .. 5, y = -6 .. 6, z = -5 .. 5, numpoints= 300, labels=[y, x,z],axes
= NORMAL);
> implicitplot3d(x =4*z^2, x = -5 .. 5, y = -5 .. 5, z = 0 ..5, numpoints=3000, labels=[y,x, z],axes=
NORMAL);
> plot3d([y*cos(x),y*sin(x),y],x = -5 .. 5, y = -5 .. 5, numpoints=3000, axes= normal);
> implicitplot3d(3*x^2+2*y^2-z^2+6*x-2*z-13 = 0, x = -5 .. 5, y = -5 .. 10, z = -5 ..5, numpoints=
3000, labels=[y,x, z],axes= NORMAL);
> implicitplot3d(x^2+y^2= (8+sqrt(3^2-z^2))^2, x = -15 ..15, y = -15 .. 15, z = -9 .. 9, numpoints=
5000, labels=[y,x, z],axes= NORMAL);
> with(Student[Calculus1]);
> SurfaceOfRevolution(8+sqrt(9-x^2),x = -7 .. 9, numpoints=500, output= plot);
> with(plottools);
[arc, arrow,circle,cone,cuboid,curve,cutin,cutout,
cylinder,disk,dodecahedron,ellipse,ellipticArc,getdata,
hemisphere,hexahedron,homothety,hyperbola,icosahedron,
line,octahedron,parallelepiped,pieslice,point,polygon,
project,rectangle,reflect,rotate,scale,semitorus,sphere,

4. stellate,tetrahedron,torus,transform, translate]
> with(plottools);
> implicitplot3d({seq(4*x-2*y+k*z= 0, k = 1 .. 6)}, x = -3 .. 3, y = -3 .. 3, z = -3 .. 3, axes= NORMAL);
> implicitplot3d({seq(3*k*x-k*y-2*z= 0, k = 1 ..6)}, x = -3 .. 3, y = -3 .. 3, z = -3 ..3, axes=
NORMAL);
> implicitplot3d(4*x^2+4*z^2 = y^2, x = -15 ..15, y = -15 ..15, z = -9 .. 9, numpoints= 5000, labels
= [y,x,z],axes= NORMAL);
>
> implicitplot3d(x^2+2*y^2 = z, x = -5 .. 5, y = -5 ..5, z = 0 .. 9, numpoints=50000, labels=[y, x,z],
axes= NORMAL);
> smartplot(x^2+y^2= 1, x^2+y^2 = 4, x^2+y^2 = 9, x^2+y^2 = 16, x^2+y^2 = 25);
> plot3d([y*cos(x),y*sin(x),y],x = -5 .. 5, y = -5 .. 5, numpoints=1000, axes= normal);
> plot3d([2*cos(x)*sin(y),4*sin(x)*sin(y),2*cos(y)],x = -5 .. 5, y = -5 .. 5, numpoints= 1000, axes=
normal);
> plot3d([4*sqrt(x)*cos(y),6*sqrt(x)*sin(y),x],x = -5 .. 5, y = -5 .. 5, numpoints=1000, axes=
normal);
> plot3d([x,y,x*y],x =-5 .. 5, y = -5 ..5, numpoints=1000, axes= normal);

5. > plot3d([2*sinh(x),4*cosh(y),x],x = -5 .. 5, y = -5 .. 5, numpoints=1000, axes= normal);
> plot3d([(8+5*cos(y))*cos(x),(8+5*cos(y))*sin(x),5*sin(x)],x = -5 .. 5, y = -5 .. 5, numpoints=
1000, axes= normal);
>