## Chapter 16

## Cylinder

##### 16.1 DEFINITION

The surface generated by a variable line which remains parallel to a fixed line and intersects a given curve (or touches a given surface) is called a cylinder.

The variable line is called the *generator,* the fixed straight line is called the *axis of the cylinder* and the given curve is called the *guiding curve of the cylinder.*

##### 16.2 EQUATION OF A CYLINDER WITH A GIVEN GENERATOR AND A GIVEN GUIDING CURVE

Let us find the equation of the cylinder whose generators are parallel to the line

and whose guiding curve is the conic

Let (*α, β, γ*) be any point on the cylinder. Then the equations of a generator are

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