Ploskve drugega reda

Elipticni stozec: x^2/a^2 + y^2/b^2 = z^2

a = 2
b = 3
ParametricPlot3D[ {{a r Cos[u], b r Sin[u], r},{a r Cos[u], b r Sin[u],-r}},{r,0,10},{u,0,2 Pi},BoxRatios->Automatic]

Elipticni paraboloid: x^2/a^2 + y^2/b^2 = z

a = 2
b = 3
ParametricPlot3D[ {{a r Cos[u], b r Sin[u], r^2}},{r,0,10},{u,0,2 Pi},BoxRatios->{1,1,1} ]

Hiperbolicni paraboloid: x^2/a^2 - y^2/b^2 = z

a = 2
b = 3
ParametricPlot3D[ {{a r Cos[u], b r Sin[u], r^2Cos[2u]}},{r,0,10},{u,0,2 Pi},BoxRatios->{1,1,1}]

Elipsoid: x^2/a^2 + y^2/b^2 + z^2/c^2 = 1

a = 2
b = 3
c = 4
ParametricPlot3D[ {{a  Cos[u]Cos[v], b  Sin[u]Cos[v], c Sin[v]}},{v,-Pi/2,Pi/2},{u,0,2 Pi},BoxRatios->Automatic]

Enodelni (elipticni) hiperboloid : x^2/a^2 + y^2/b^2 - z^2/c^2 = 1

a = 2
b = 3
c = 4
ParametricPlot3D[ {{a r Cos[u], b  r Sin[u], c Sqrt[( r^2- 1)]},{a r Cos[u], b  r Sin[u],- c Sqrt[( r^2- 1)]}},{r,0,5},{u,0,2 Pi},BoxRatios->{1,1,1}]

Dvodelni (elipticni) hiperboloid : x^2/a^2 + y^2/b^2 - z^2/c^2 = -1

a = 2
b = 3
c = 4
ParametricPlot3D[ {{a r Cos[u], b  r Sin[u], c Sqrt[( r^2+ 1)]},{a r Cos[u], b  r Sin[u],- c Sqrt[( r^2+ 1)]}},{r,0,5},{u,0,2 Pi},BoxRatios->{1,1,1}]