MHB Elliptic Cylinder: What Determines Radius & Height?

[Yankel]

Hello all,

I have a theoretical question. This is the formula for an elliptic cylinder (right?)

\[\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1\]

I understand that the point (a,b) represent the center of the basic ellipse of the cylinder. What in the formula represent the radius of the basic ellipse ? What determines the height of the cylinder ?

In other words, if I have two cylinders, let's say both with a base centered at (1,1), but one has a radius of 2 and height 1, and the other radius 5 with height 4, how will the equations differ ?

Many thanks !

 

[MarkFL]

The ellipse does not have a radius, but rather major and minor axes. The center of the cross-sections of the cylinder you cite is at the origin, not $(a,b)$. An ellipse in two dimensions centered at $(h,k)$ is given by:

$$\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1$$

To denote the height of the cylinder, you could place a restriction on $z$, such as $0\le z\le h$.