Cylinders

  • A cylinder is the set of all lines passing through a curve and parallel to a given line. The given line is called the axis of the cylinder and the given curve is called the base curve or directrix of the cylinder.

  • A cylinder whose base curve is a circle and whose axis passes through the center of the circle and is perpendicular to the plane of the curve is called a right circular cylinder.

  • The equation of a right circular cylinder with base curve's radius is r and whose axis z = 0 passes through (0,0,0) is
    x2 + y2 = r2.

  • The equation of a right circular cylinder with radius r and axis
    (x - a)/α = (y - b)/β = (z - c)/γ is
    [(x - a)2 + (y - b)2 + (z - c)2 - r2](α2 + β2 + γ2) = [(x - a)α + (y - b)β + (z - c)γ]2.




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