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Analytical Geometry by P. R. Vittal

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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

Equation

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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