Cone - Three dimensional spaces

The below equation is the general equation of a cone.

X² / a² + y²/b² = z²/c²

Here is a diagram of a typical cone.

Notice that this is the equation of a cone which will open along the z-axis.  To obtain the equation of a cone that opens along one of the other axes all there is a requirement to do is make a slight modification of the equation.  This will be the example for the rest of the surfaces that we'll be looking at in this part also.

In the case of a cone the variable which sits by itself on one side of the equal sign will determine the axis that the cone opens up along.  For example, a cone that opens up along the x-axis will comprise the equation,

y²/ b² + z²/c² = x²/a² 

For several surfaces we will not give the other possible formulas. Though we will acknowledge how each formula requires to be changed to get a change of orientation for the surface.