1) Elliptic paraboloid x^2 / a^2 + y^2/b^2 = z/c
where z determine the axis upon which the paraboloid opens up.
The sign of c determine the direction that paraboloid opens up,
2) Hyperboloid paraboloid ---- x^2/a^2 - y^2/b^2 = z/c
Agian c will determine the direction that the surface opens up.
3) Ellipsoid --- x^2/a^2 + y^2/b^2 + z^2/c^2 = 1
Note: if a = b = c then it becomes a sphere.
4) Cone ---- x^2/a^2 + y^2/b^2 = z^2 / c^2
where the variable at RHS, z in this case, determine the axis that the cone opens up along.
5) Ellipse --- a(x-b)^2 + c(y-d)^2 = r^2Note; If a = c, It become circle with center at (b,d) and radius, r
Hope this will help you to solve your tutorial question on level curves and surfaces.
