# Equation for elliptic cylinder

• Somefantastik
In summary, the conversation discussed adding a constraint to the equation for an elliptic cylinder to ensure that it lies above the plane z = -1. It was suggested to specify the z domain or define a function of z to indicate where the cylinder exists. The equation for the cylinder does not involve z, but it can be incorporated into the equation by replacing the value of 1 with a function of z. This clarification was helpful to the person seeking assistance.
Somefantastik
I know that the equation for an elliptic cylinder is

$$\frac{{\left( {x - x_0 } \right)^2 }}{{a^2 }} + \frac{{\left( {y - y_0 } \right)^2 }}{{b^2 }} = 1$$

How do I add a constraint on that to make sure that it lies above the plane z = -1? I'm confused about it b/c its equation does not involve z (a degenerate quadric?)

You just have to specify the z domain for which the equation applies. If you insist on having one equation, define a function of z where f(z)=1 where the cylinder is supposed to exist and f(z)=-1 otherwise. Then in the ellipse equation, replace = 1 by = f(z).

Ok, that helps, thank you.

## 1. What is the equation for an elliptic cylinder?

The equation for an elliptic cylinder is x2/a2 + y2/b2 = 1, where a and b are the radii of the ellipse in the x and y directions, respectively.

## 2. How is an elliptic cylinder different from a circular cylinder?

An elliptic cylinder has an elliptical cross-section, while a circular cylinder has a circular cross-section. This means that the radius of the cylinder varies depending on the direction, whereas a circular cylinder has a constant radius.

## 3. Can an elliptic cylinder have negative radii?

Yes, an elliptic cylinder can have negative radii. This would result in a "flipped" or inverted ellipse, where the major and minor axes are swapped in position.

## 4. What is the volume of an elliptic cylinder?

The volume of an elliptic cylinder is given by the formula V = πabh, where a and b are the radii of the ellipse and h is the height of the cylinder.

## 5. How is an elliptic cylinder used in real life?

Elliptic cylinders are used in various engineering applications, such as in the design of pipes, tunnels, and pressure vessels. They are also used in architecture, such as in the construction of domes and arches. In addition, elliptic cylinders are used in mathematical modeling and simulations in fields such as physics and astrophysics.

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