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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.
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