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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 !