Quadratic Surfaces

Explore the six types of quadratic surfaces given below:

Ellipsoid: ((x^2)/(a^2))+((y^2)/(b^2))+((z^2)/(c^2))=1

a=1;
b=2;
c=3;
ContourPlot3D[1-z^2/c^2-x^2/a^2-y^2/b^2,{x,-3,3},{y,-3,3},{z,-3,3},Contours->{0.},AxesLabel->{x,y,z}]

Elliptic Paraboloid: (z/c)=((x^2)/(a^2))+((y^2)/(b^2))

a=1;
b=2;
c=3;
ContourPlot3D[z/c-x^2/a^2-y^2/b^2,{x,-2,2},{y,-2,2},{z,-3,3},Contours->{0.},AxesLabel->{x,y,z}]

Hyperbolic paraboloid: (z/c)=((x^2)/(a^2))-((y^2)/(b^2))

a=1;
b=2;
c=3;
ContourPlot3D[z/c-x^2/a^2+y^2/b^2,{x,-1,1},{y,-1,1},{z,-1,1},Contours->{0.},AxesLabel->{x,y,z}]

Cone: ((z^2)/(c^2))=((x^2)/(a^2))+((y^2)/(b^2))

a=1;
b=2;
c=3;
ContourPlot3D[z^2/c^2-x^2/a^2-y^2/b^2,{x,-1,1},{y,-1,1},{z,-1,1},Contours->{0.},AxesLabel->{x,y,z}]

Hyperboloid of one sheet: ((x^2)/(a^2))+((y^2)/(b^2))-((z^2)/(c^2))=1

a=1;
b=2;
c=3;
ContourPlot3D[1+z^2/c^2-x^2/a^2-y^2/b^2,{x,-5,5},{y,-5,5},{z,-5,5},Contours->{0.},AxesLabel->{x,y,z}]

Hyperboloid of two sheets: -((x^2)/(a^2))-((y^2)/(b^2))+((z^2)/(c^2))=1

a=1;
b=2;
c=3;
ContourPlot3D[1-z^2/c^2+x^2/a^2+y^2/b^2,{x,-10,10},{y,-10,10},{z,-10,10},Contours->{0.},AxesLabel->{x,y,z}]